x^2=-19x-90

Solution for x^2=-19x-90 equation:

Simplifying
x2 = -19x + -90

Reorder the terms:
x2 = -90 + -19x

Solving
x2 = -90 + -19x

Solving for variable 'x'.

Reorder the terms:
90 + 19x + x2 = -90 + -19x + 90 + 19x

Reorder the terms:
90 + 19x + x2 = -90 + 90 + -19x + 19x

Combine like terms: -90 + 90 = 0
90 + 19x + x2 = 0 + -19x + 19x
90 + 19x + x2 = -19x + 19x

Combine like terms: -19x + 19x = 0
90 + 19x + x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

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