=x^2+23x+90

Solution for =x^2+23x+90 equation:

Simplifying
0 = x2 + 23x + 90

Reorder the terms:
0 = 90 + 23x + x2

Solving
0 = 90 + 23x + x2

Solving for variable 'x'.

Combine like terms: 0 + -90 = -90
-90 + -23x + -1x2 = 90 + 23x + x2 + -90 + -23x + -1x2

Reorder the terms:
-90 + -23x + -1x2 = 90 + -90 + 23x + -23x + x2 + -1x2

Combine like terms: 90 + -90 = 0
-90 + -23x + -1x2 = 0 + 23x + -23x + x2 + -1x2
-90 + -23x + -1x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
-90 + -23x + -1x2 = 0 + x2 + -1x2
-90 + -23x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-90 + -23x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(90 + 23x + x2) = 0

Factor a trinomial.
-1((18 + x)(5 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-18, -5}