Solve (x-7)(x+2)=-5(x+2)

$$( x - 7 ) ( x + 2 ) = - 5 ( x + 2 )$$

Solve for x

$$x=-2$$

$$x=2$$

Steps by Finding Square Root

Use the distributive property to multiply x-7 by x+2 and combine like terms.

$$x^{2}-5x-14=-5\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$x^{2}-5x-14=-5x-10$$

Add 5x to both sides.

$$x^{2}-5x-14+5x=-10$$

Combine -5x and 5x to get 0.

$$x^{2}-14=-10$$

Add 14 to both sides.

$$x^{2}=-10+14$$

Add -10 and 14 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-7 by x+2 and combine like terms.

$$x^{2}-5x-14=-5\left(x+2\right)$$

Use the distributive property to multiply -5 by x+2.

$$x^{2}-5x-14=-5x-10$$

Add 5x to both sides.

$$x^{2}-5x-14+5x=-10$$

Combine -5x and 5x to get 0.

$$x^{2}-14=-10$$

Add 10 to both sides.

$$x^{2}-14+10=0$$

Add -14 and 10 to get -4.

$$x^{2}-4=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)}}{2}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16}}{2}$$

Take the square root of 16.

$$x=\frac{0±4}{2}$$

Now solve the equation x=\frac{0±4}{2} when ± is plus. Divide 4 by 2.

$$x=2$$

Now solve the equation x=\frac{0±4}{2} when ± is minus. Divide -4 by 2.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$