Solve (x+2)(x+3)=5(x+3)

$$( x + 2 ) ( x + 3 ) = 5 ( x + 3 )$$

Solve for x

$$x=-3$$

$$x=3$$

Steps by Finding Square Root

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

$$x^{2}+5x+6=5\left(x+3\right)$$

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

$$x^{2}+5x+6=5x+15$$

Subtract 5x from both sides.

$$x^{2}+5x+6-5x=15$$

Combine 5x and -5x to get 0.

$$x^{2}+6=15$$

Subtract 6 from both sides.

$$x^{2}=15-6$$

Subtract 6 from 15 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

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

$$x^{2}+5x+6=5\left(x+3\right)$$

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

$$x^{2}+5x+6=5x+15$$

Subtract 5x from both sides.

$$x^{2}+5x+6-5x=15$$

Combine 5x and -5x to get 0.

$$x^{2}+6=15$$

Subtract 15 from both sides.

$$x^{2}+6-15=0$$

Subtract 15 from 6 to get -9.

$$x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$x=\frac{0±6}{2}$$

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

$$x=3$$

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

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$