Solve (m+4)(4m-2)=5(m+3)-10

$$( m + 4 ) ( 4 m - 2 ) = 5 ( m + 3 ) - 10$$

Solve for m

$$m = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

$$m=1$$

Steps Using the Quadratic Formula

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

$$4m^{2}+14m-8=5\left(m+3\right)-10$$

Use the distributive property to multiply 5 by m+3.

$$4m^{2}+14m-8=5m+15-10$$

Subtract 10 from 15 to get 5.

$$4m^{2}+14m-8=5m+5$$

Subtract 5m from both sides.

$$4m^{2}+14m-8-5m=5$$

Combine 14m and -5m to get 9m.

$$4m^{2}+9m-8=5$$

Subtract 5 from both sides.

$$4m^{2}+9m-8-5=0$$

Subtract 5 from -8 to get -13.

$$4m^{2}+9m-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 9 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-9±\sqrt{9^{2}-4\times 4\left(-13\right)}}{2\times 4}$$

Square 9.

$$m=\frac{-9±\sqrt{81-4\times 4\left(-13\right)}}{2\times 4}$$

Multiply -4 times 4.

$$m=\frac{-9±\sqrt{81-16\left(-13\right)}}{2\times 4}$$

Multiply -16 times -13.

$$m=\frac{-9±\sqrt{81+208}}{2\times 4}$$

Add 81 to 208.

$$m=\frac{-9±\sqrt{289}}{2\times 4}$$

Take the square root of 289.

$$m=\frac{-9±17}{2\times 4}$$

Multiply 2 times 4.

$$m=\frac{-9±17}{8}$$

Now solve the equation m=\frac{-9±17}{8} when ± is plus. Add -9 to 17.

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

Divide 8 by 8.

$$m=1$$

Now solve the equation m=\frac{-9±17}{8} when ± is minus. Subtract 17 from -9.

$$m=-\frac{26}{8}$$

Reduce the fraction \frac{-26}{8} to lowest terms by extracting and canceling out 2.

$$m=-\frac{13}{4}$$

The equation is now solved.

$$m=1 m=-\frac{13}{4}$$

Steps for Completing the Square

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

$$4m^{2}+14m-8=5\left(m+3\right)-10$$

Use the distributive property to multiply 5 by m+3.

$$4m^{2}+14m-8=5m+15-10$$

Subtract 10 from 15 to get 5.

$$4m^{2}+14m-8=5m+5$$

Subtract 5m from both sides.

$$4m^{2}+14m-8-5m=5$$

Combine 14m and -5m to get 9m.

$$4m^{2}+9m-8=5$$

Add 8 to both sides.

$$4m^{2}+9m=5+8$$

Add 5 and 8 to get 13.

$$4m^{2}+9m=13$$

Divide both sides by 4.

$$\frac{4m^{2}+9m}{4}=\frac{13}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$m^{2}+\frac{9}{4}m=\frac{13}{4}$$

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.

$$m^{2}+\frac{9}{4}m+\left(\frac{9}{8}\right)^{2}=\frac{13}{4}+\left(\frac{9}{8}\right)^{2}$$

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

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{13}{4}+\frac{81}{64}$$

Add \frac{13}{4} to \frac{81}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$m^{2}+\frac{9}{4}m+\frac{81}{64}=\frac{289}{64}$$

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}.

$$\left(m+\frac{9}{8}\right)^{2}=\frac{289}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+\frac{9}{8}\right)^{2}}=\sqrt{\frac{289}{64}}$$

Simplify.

$$m+\frac{9}{8}=\frac{17}{8} m+\frac{9}{8}=-\frac{17}{8}$$

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

$$m=1 m=-\frac{13}{4}$$