Solve 6a^2-12a

$$6 a ^ { 2 } - 12 a$$

Factor

$$6a\left(a-2\right)$$

Solution Steps

Factor out 6.

$$6\left(a^{2}-2a\right)$$

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

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

Rewrite the complete factored expression.

$$6a\left(a-2\right)$$

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.

$$6a^{2}-12a=0$$

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.

$$a=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 6}$$

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

$$a=\frac{-\left(-12\right)±12}{2\times 6}$$

The opposite of -12 is 12.

$$a=\frac{12±12}{2\times 6}$$

Multiply 2 times 6.

$$a=\frac{12±12}{12}$$

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

$$a=\frac{24}{12}$$

Divide 24 by 12.

$$a=2$$

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

$$a=\frac{0}{12}$$

Divide 0 by 12.

$$a=0$$

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

$$6a^{2}-12a=6\left(a-2\right)a$$

Evaluate

$$6a\left(a-2\right)$$