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

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

Solve for m

$$m=-1$$

$$m=2$$

Steps Using the Quadratic Formula

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

$$m^{2}-m-6=-4$$

Add 4 to both sides.

$$m^{2}-m-6+4=0$$

Add -6 and 4 to get -2.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -1 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Multiply -4 times -2.

$$m=\frac{-\left(-1\right)±\sqrt{1+8}}{2}$$

Add 1 to 8.

$$m=\frac{-\left(-1\right)±\sqrt{9}}{2}$$

Take the square root of 9.

$$m=\frac{-\left(-1\right)±3}{2}$$

The opposite of -1 is 1.

$$m=\frac{1±3}{2}$$

Now solve the equation m=\frac{1±3}{2} when ± is plus. Add 1 to 3.

$$m=\frac{4}{2}$$

Divide 4 by 2.

$$m=2$$

Now solve the equation m=\frac{1±3}{2} when ± is minus. Subtract 3 from 1.

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

Divide -2 by 2.

$$m=-1$$

The equation is now solved.

$$m=2 m=-1$$

Steps for Completing the Square

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

$$m^{2}-m-6=-4$$

Add 6 to both sides.

$$m^{2}-m=-4+6$$

Add -4 and 6 to get 2.

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

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

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-m+\frac{1}{4}=2+\frac{1}{4}$$

Add 2 to \frac{1}{4}.

$$m^{2}-m+\frac{1}{4}=\frac{9}{4}$$

Factor m^{2}-m+\frac{1}{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}.

$$\left(m-\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$m-\frac{1}{2}=\frac{3}{2} m-\frac{1}{2}=-\frac{3}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$m=2 m=-1$$