Solve 12m^2=m(4m+4)

$$12 m ^ { 2 } = m ( 4 m + 4 )$$

Solve for m

$$m=\frac{1}{2}=0.5$$

$$m=0$$

Steps Using Factoring

Use the distributive property to multiply m by 4m+4.

$$12m^{2}=4m^{2}+4m$$

Subtract 4m^{2} from both sides.

$$12m^{2}-4m^{2}=4m$$

Combine 12m^{2} and -4m^{2} to get 8m^{2}.

$$8m^{2}=4m$$

Subtract 4m from both sides.

$$8m^{2}-4m=0$$

Factor out m.

$$m\left(8m-4\right)=0$$

To find equation solutions, solve m=0 and 8m-4=0.

$$m=0 m=\frac{1}{2}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply m by 4m+4.

$$12m^{2}=4m^{2}+4m$$

Subtract 4m^{2} from both sides.

$$12m^{2}-4m^{2}=4m$$

Combine 12m^{2} and -4m^{2} to get 8m^{2}.

$$8m^{2}=4m$$

Subtract 4m from both sides.

$$8m^{2}-4m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -4 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\times 8}$$

Take the square root of \left(-4\right)^{2}.

$$m=\frac{-\left(-4\right)±4}{2\times 8}$$

The opposite of -4 is 4.

$$m=\frac{4±4}{2\times 8}$$

Multiply 2 times 8.

$$m=\frac{4±4}{16}$$

Now solve the equation m=\frac{4±4}{16} when ± is plus. Add 4 to 4.

$$m=\frac{8}{16}$$

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

$$m=\frac{1}{2}$$

Now solve the equation m=\frac{4±4}{16} when ± is minus. Subtract 4 from 4.

$$m=\frac{0}{16}$$

Divide 0 by 16.

$$m=0$$

The equation is now solved.

$$m=\frac{1}{2} m=0$$

Steps for Completing the Square

Use the distributive property to multiply m by 4m+4.

$$12m^{2}=4m^{2}+4m$$

Subtract 4m^{2} from both sides.

$$12m^{2}-4m^{2}=4m$$

Combine 12m^{2} and -4m^{2} to get 8m^{2}.

$$8m^{2}=4m$$

Subtract 4m from both sides.

$$8m^{2}-4m=0$$

Divide both sides by 8.

$$\frac{8m^{2}-4m}{8}=\frac{0}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$m^{2}+\left(-\frac{4}{8}\right)m=\frac{0}{8}$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$m^{2}-\frac{1}{2}m=\frac{0}{8}$$

Divide 0 by 8.

$$m^{2}-\frac{1}{2}m=0$$

Divide -\frac{1}{2}, the coefficient of the x term, by 2 to get -\frac{1}{4}. Then add the square of -\frac{1}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{1}{2}m+\left(-\frac{1}{4}\right)^{2}=\left(-\frac{1}{4}\right)^{2}$$

Square -\frac{1}{4} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{1}{2}m+\frac{1}{16}=\frac{1}{16}$$

Factor m^{2}-\frac{1}{2}m+\frac{1}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{1}{4}\right)^{2}=\frac{1}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{1}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Simplify.

$$m-\frac{1}{4}=\frac{1}{4} m-\frac{1}{4}=-\frac{1}{4}$$

Add \frac{1}{4} to both sides of the equation.

$$m=\frac{1}{2} m=0$$