Solve 3a^2-6a

$$3 a ^ { 2 } - 6 a$$

Factor

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

Solution Steps

Factor out 3.

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

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

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

Rewrite the complete factored expression.

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

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.

$$3a^{2}-6a=0$$

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.

$$a=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 3}$$

Take the square root of \left(-6\right)^{2}.

$$a=\frac{-\left(-6\right)±6}{2\times 3}$$

The opposite of -6 is 6.

$$a=\frac{6±6}{2\times 3}$$

Multiply 2 times 3.

$$a=\frac{6±6}{6}$$

Now solve the equation a=\frac{6±6}{6} when ± is plus. Add 6 to 6.

$$a=\frac{12}{6}$$

Divide 12 by 6.

$$a=2$$

Now solve the equation a=\frac{6±6}{6} when ± is minus. Subtract 6 from 6.

$$a=\frac{0}{6}$$

Divide 0 by 6.

$$a=0$$

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}.

$$3a^{2}-6a=3\left(a-2\right)a$$

Evaluate

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