0=x^2+x-90

Solution for 0=x^2+x-90 equation:

Simplifying
0 = x2 + x + -90

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

Solving
0 = -90 + x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(9 + -1x)(10 + x) = 0

Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

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

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

Simplifying
x = -10
Solution
x = {9, -10}