x^2=9x+90

Solution for x^2=9x+90 equation:

Simplifying
x2 = 9x + 90

Reorder the terms:
x2 = 90 + 9x

Solving
x2 = 90 + 9x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(-6 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-6, 15}