(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 = -1x
(-20 + -1x + x2) = 90

Solving
-20 + -1x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-20 + -90 + -1x + x2 = 90 + -90

Combine like terms: -20 + -90 = -110
-110 + -1x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-110 + -1x + x2 = 0

Factor a trinomial.
(-10 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-10, 11}