(x+2)(x+3)=90

Solution for (x+2)(x+3)=90 equation:

Simplifying
(x + 2)(x + 3) = 90

Reorder the terms:
(2 + x)(x + 3) = 90

Reorder the terms:
(2 + x)(3 + x) = 90

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 90
((3 * 2 + x * 2) + x(3 + x)) = 90
((6 + 2x) + x(3 + x)) = 90
(6 + 2x + (3 * x + x * x)) = 90
(6 + 2x + (3x + x2)) = 90

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 90

Solving
6 + 5x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
6 + -90 + 5x + x2 = 90 + -90

Combine like terms: 6 + -90 = -84
-84 + 5x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-84 + 5x + x2 = 0

Factor a trinomial.
(-12 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-12, 7}