x^2+18x=-77

Solution for x^2+18x=-77 equation:

Simplifying
x2 + 18x = -77

Reorder the terms:
18x + x2 = -77

Solving
18x + x2 = -77

Solving for variable 'x'.

Reorder the terms:
77 + 18x + x2 = -77 + 77

Combine like terms: -77 + 77 = 0
77 + 18x + x2 = 0

Factor a trinomial.
(11 + x)(7 + x) = 0

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {-11, -7}