x^2+90x+89=0

Solution for x^2+90x+89=0 equation:

Simplifying
x2 + 90x + 89 = 0

Reorder the terms:
89 + 90x + x2 = 0

Solving
89 + 90x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(89 + x)(1 + x) = 0

Subproblem 1
Set the factor '(89 + x)' equal to zero and attempt to solve:

Simplifying
89 + x = 0

Solving
89 + x = 0

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

Add '-89' to each side of the equation.
89 + -89 + x = 0 + -89

Combine like terms: 89 + -89 = 0
0 + x = 0 + -89
x = 0 + -89

Combine like terms: 0 + -89 = -89
x = -89

Simplifying
x = -89
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-89, -1}