Solve (x+2)(x-3)=-x

$$(x+2)(x-3)=-x$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

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

$$x^{2}-x-6=-x$$

Add x to both sides.

$$x^{2}-x-6+x=0$$

Combine -x and x to get 0.

$$x^{2}-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

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

$$x^{2}-x-6=-x$$

Add x to both sides.

$$x^{2}-x-6+x=0$$

Combine -x and x to get 0.

$$x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$