Solve 3m^2-6m

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

Factor

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

Solution Steps

Factor out 3.

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

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

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

Rewrite the complete factored expression.

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

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.

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

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.

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

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

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

The opposite of -6 is 6.

$$m=\frac{6±6}{2\times 3}$$

Multiply 2 times 3.

$$m=\frac{6±6}{6}$$

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

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

Divide 12 by 6.

$$m=2$$

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

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

Divide 0 by 6.

$$m=0$$

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}.

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

Evaluate

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