Solve 16=4(m-2)(2m-6)

$$16 = 4 ( m - 2 ) ( 2 m - 6 )$$

Solve for m

$$m=1$$

$$m=4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4 by m-2.

$$16=\left(4m-8\right)\left(2m-6\right)$$

Use the distributive property to multiply 4m-8 by 2m-6 and combine like terms.

$$16=8m^{2}-40m+48$$

Swap sides so that all variable terms are on the left hand side.

$$8m^{2}-40m+48=16$$

Subtract 16 from both sides.

$$8m^{2}-40m+48-16=0$$

Subtract 16 from 48 to get 32.

$$8m^{2}-40m+32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, -40 for b, and 32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 8\times 32}}{2\times 8}$$

Square -40.

$$m=\frac{-\left(-40\right)±\sqrt{1600-4\times 8\times 32}}{2\times 8}$$

Multiply -4 times 8.

$$m=\frac{-\left(-40\right)±\sqrt{1600-32\times 32}}{2\times 8}$$

Multiply -32 times 32.

$$m=\frac{-\left(-40\right)±\sqrt{1600-1024}}{2\times 8}$$

Add 1600 to -1024.

$$m=\frac{-\left(-40\right)±\sqrt{576}}{2\times 8}$$

Take the square root of 576.

$$m=\frac{-\left(-40\right)±24}{2\times 8}$$

The opposite of -40 is 40.

$$m=\frac{40±24}{2\times 8}$$

Multiply 2 times 8.

$$m=\frac{40±24}{16}$$

Now solve the equation m=\frac{40±24}{16} when ± is plus. Add 40 to 24.

$$m=\frac{64}{16}$$

Divide 64 by 16.

$$m=4$$

Now solve the equation m=\frac{40±24}{16} when ± is minus. Subtract 24 from 40.

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

Divide 16 by 16.

$$m=1$$

The equation is now solved.

$$m=4 m=1$$

Steps for Completing the Square

Use the distributive property to multiply 4 by m-2.

$$16=\left(4m-8\right)\left(2m-6\right)$$

Use the distributive property to multiply 4m-8 by 2m-6 and combine like terms.

$$16=8m^{2}-40m+48$$

Swap sides so that all variable terms are on the left hand side.

$$8m^{2}-40m+48=16$$

Subtract 48 from both sides.

$$8m^{2}-40m=16-48$$

Subtract 48 from 16 to get -32.

$$8m^{2}-40m=-32$$

Divide both sides by 8.

$$\frac{8m^{2}-40m}{8}=-\frac{32}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$m^{2}+\left(-\frac{40}{8}\right)m=-\frac{32}{8}$$

Divide -40 by 8.

$$m^{2}-5m=-\frac{32}{8}$$

Divide -32 by 8.

$$m^{2}-5m=-4$$

Divide -5, the coefficient of the x term, by 2 to get -\frac{5}{2}. Then add the square of -\frac{5}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-5m+\left(-\frac{5}{2}\right)^{2}=-4+\left(-\frac{5}{2}\right)^{2}$$

Square -\frac{5}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-5m+\frac{25}{4}=-4+\frac{25}{4}$$

Add -4 to \frac{25}{4}.

$$m^{2}-5m+\frac{25}{4}=\frac{9}{4}$$

Factor m^{2}-5m+\frac{25}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{5}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{5}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$m-\frac{5}{2}=\frac{3}{2} m-\frac{5}{2}=-\frac{3}{2}$$

Add \frac{5}{2} to both sides of the equation.

$$m=4 m=1$$