Factor <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>12</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>16</mn><mi>x</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mrow><mo>(</mo><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mo>-</mo><mi>x</mi><mrow><mo>(</mo><mn>12</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mrow><mo>(</mo><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mi>x</mi><mrow><mo>(</mo><mo>-</mo><mn>16</mn><mo>)</mo></mrow></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>-</mo><mn>16</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>-</mo><mn>16</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Use the quadratic formula to find the solutions.

Substitute the values <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mn>19</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>12</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>c</mi><mo>=</mo><mo>-</mo><mn>16</mn></mstyle></math> into the quadratic formula and solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

Simplify.

Simplify the numerator.

Raise <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>76</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>16</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1216</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1360</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><mn>85</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>1360</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>19</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>12</mn><mo>±</mo><mn>4</mn><msqrt><mn>85</mn></msqrt></mrow><mrow><mn>38</mn></mrow></mfrac></mstyle></math> .

The final answer is the combination of both solutions.

The final solution is all the values that make <math><mstyle displaystyle="true"><mo>-</mo><mi>x</mi><mrow><mo>(</mo><mn>19</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>-</mo><mn>16</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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