(x+4)(x+5)=90

Solution for (x+4)(x+5)=90 equation:

Simplifying
(x + 4)(x + 5) = 90

Reorder the terms:
(4 + x)(x + 5) = 90

Reorder the terms:
(4 + x)(5 + x) = 90

Multiply (4 + x) * (5 + x)
(4(5 + x) + x(5 + x)) = 90
((5 * 4 + x * 4) + x(5 + x)) = 90
((20 + 4x) + x(5 + x)) = 90
(20 + 4x + (5 * x + x * x)) = 90
(20 + 4x + (5x + x2)) = 90

Combine like terms: 4x + 5x = 9x
(20 + 9x + x2) = 90

Solving
20 + 9x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
20 + -90 + 9x + x2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + 9x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + 9x + x2 = 0

Factor a trinomial.
(-14 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-14, 5}