(x+2)(x+3)-5(x+3)=0

Solution for (x+2)(x+3)-5(x+3)=0 equation:

Simplifying
(x + 2)(x + 3) + -5(x + 3) = 0

Reorder the terms:
(2 + x)(x + 3) + -5(x + 3) = 0

Reorder the terms:
(2 + x)(3 + x) + -5(x + 3) = 0

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) + -5(x + 3) = 0
((3 * 2 + x * 2) + x(3 + x)) + -5(x + 3) = 0
((6 + 2x) + x(3 + x)) + -5(x + 3) = 0
(6 + 2x + (3 * x + x * x)) + -5(x + 3) = 0
(6 + 2x + (3x + x2)) + -5(x + 3) = 0

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) + -5(x + 3) = 0

Reorder the terms:
6 + 5x + x2 + -5(3 + x) = 0
6 + 5x + x2 + (3 * -5 + x * -5) = 0
6 + 5x + x2 + (-15 + -5x) = 0

Reorder the terms:
6 + -15 + 5x + -5x + x2 = 0

Combine like terms: 6 + -15 = -9
-9 + 5x + -5x + x2 = 0

Combine like terms: 5x + -5x = 0
-9 + 0 + x2 = 0
-9 + x2 = 0

Solving
-9 + x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x2 = 0 + 9
x2 = 0 + 9

Combine like terms: 0 + 9 = 9
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}