Solve -12a-8a^2

$$- 12 a - 8 a ^ { 2 }$$

Factor

$$-4a\left(2a+3\right)$$

Solution Steps

Factor out 4.

$$4\left(-3a-2a^{2}\right)$$

Consider -3a-2a^{2}. Factor out a.

$$a\left(-3-2a\right)$$

Rewrite the complete factored expression.

$$4a\left(-2a-3\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-8a^{2}-12a=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$a=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\left(-8\right)}$$

Take the square root of \left(-12\right)^{2}.

$$a=\frac{-\left(-12\right)±12}{2\left(-8\right)}$$

The opposite of -12 is 12.

$$a=\frac{12±12}{2\left(-8\right)}$$

Multiply 2 times -8.

$$a=\frac{12±12}{-16}$$

Now solve the equation a=\frac{12±12}{-16} when ± is plus. Add 12 to 12.

$$a=\frac{24}{-16}$$

Reduce the fraction \frac{24}{-16} to lowest terms by extracting and canceling out 8.

$$a=-\frac{3}{2}$$

Now solve the equation a=\frac{12±12}{-16} when ± is minus. Subtract 12 from 12.

$$a=\frac{0}{-16}$$

Divide 0 by -16.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{3}{2} for x_{1} and 0 for x_{2}.

$$-8a^{2}-12a=-8\left(a-\left(-\frac{3}{2}\right)\right)a$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$-8a^{2}-12a=-8\left(a+\frac{3}{2}\right)a$$

Add \frac{3}{2} to a by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$-8a^{2}-12a=-8\times \frac{-2a-3}{-2}a$$

Cancel out 2, the greatest common factor in -8 and -2.

$$-8a^{2}-12a=4\left(-2a-3\right)a$$

Evaluate

$$-4a\left(2a+3\right)$$