Solve 36m=(6-2m)(4m+3)

$$36 m = ( 6 - 2 m ) ( 4 m + 3 )$$

Solve for m

$$m=-3$$

$$m=\frac{3}{4}=0.75$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 6-2m by 4m+3 and combine like terms.

$$36m=18m+18-8m^{2}$$

Subtract 18m from both sides.

$$36m-18m=18-8m^{2}$$

Combine 36m and -18m to get 18m.

$$18m=18-8m^{2}$$

Subtract 18 from both sides.

$$18m-18=-8m^{2}$$

Add 8m^{2} to both sides.

$$18m-18+8m^{2}=0$$

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.

$$8m^{2}+18m-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 18 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-18±\sqrt{18^{2}-4\times 8\left(-18\right)}}{2\times 8}$$

Square 18.

$$m=\frac{-18±\sqrt{324-4\times 8\left(-18\right)}}{2\times 8}$$

Multiply -4 times 8.

$$m=\frac{-18±\sqrt{324-32\left(-18\right)}}{2\times 8}$$

Multiply -32 times -18.

$$m=\frac{-18±\sqrt{324+576}}{2\times 8}$$

Add 324 to 576.

$$m=\frac{-18±\sqrt{900}}{2\times 8}$$

Take the square root of 900.

$$m=\frac{-18±30}{2\times 8}$$

Multiply 2 times 8.

$$m=\frac{-18±30}{16}$$

Now solve the equation m=\frac{-18±30}{16} when ± is plus. Add -18 to 30.

$$m=\frac{12}{16}$$

Reduce the fraction \frac{12}{16} to lowest terms by extracting and canceling out 4.

$$m=\frac{3}{4}$$

Now solve the equation m=\frac{-18±30}{16} when ± is minus. Subtract 30 from -18.

$$m=-\frac{48}{16}$$

Divide -48 by 16.

$$m=-3$$

The equation is now solved.

$$m=\frac{3}{4} m=-3$$

Steps for Completing the Square

Use the distributive property to multiply 6-2m by 4m+3 and combine like terms.

$$36m=18m+18-8m^{2}$$

Subtract 18m from both sides.

$$36m-18m=18-8m^{2}$$

Combine 36m and -18m to get 18m.

$$18m=18-8m^{2}$$

Add 8m^{2} to both sides.

$$18m+8m^{2}=18$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$8m^{2}+18m=18$$

Divide both sides by 8.

$$\frac{8m^{2}+18m}{8}=\frac{18}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$m^{2}+\frac{18}{8}m=\frac{18}{8}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

$$m^{2}+\frac{9}{4}m=\frac{18}{8}$$

Reduce the fraction \frac{18}{8} to lowest terms by extracting and canceling out 2.

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

Divide \frac{9}{4}, the coefficient of the x term, by 2 to get \frac{9}{8}. Then add the square of \frac{9}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}+\frac{9}{4}m+\left(\frac{9}{8}\right)^{2}=\frac{9}{4}+\left(\frac{9}{8}\right)^{2}$$

Square \frac{9}{8} by squaring both the numerator and the denominator of the fraction.

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{9}{4}+\frac{81}{64}$$

Add \frac{9}{4} to \frac{81}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{225}{64}$$

Factor m^{2}+\frac{9}{4}m+\frac{81}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+\frac{9}{8}\right)^{2}=\frac{225}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+\frac{9}{8}\right)^{2}}=\sqrt{\frac{225}{64}}$$

Simplify.

$$m+\frac{9}{8}=\frac{15}{8} m+\frac{9}{8}=-\frac{15}{8}$$

Subtract \frac{9}{8} from both sides of the equation.

$$m=\frac{3}{4} m=-3$$