Solve 12a-8a^2=

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

Factor

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

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.

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

Take the square root of 12^{2}.

$$a=\frac{-12±12}{2\left(-8\right)}$$

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.

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

Divide 0 by -16.

$$a=0$$

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

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

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

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

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

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

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

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

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

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

Evaluate

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