117=x^2+18x+77

Solution for 117=x^2+18x+77 equation:

Simplifying
117 = x2 + 18x + 77

Reorder the terms:
117 = 77 + 18x + x2

Solving
117 = 77 + 18x + x2

Solving for variable 'x'.

Combine like terms: 117 + -77 = 40
40 + -18x + -1x2 = 77 + 18x + x2 + -77 + -18x + -1x2

Reorder the terms:
40 + -18x + -1x2 = 77 + -77 + 18x + -18x + x2 + -1x2

Combine like terms: 77 + -77 = 0
40 + -18x + -1x2 = 0 + 18x + -18x + x2 + -1x2
40 + -18x + -1x2 = 18x + -18x + x2 + -1x2

Combine like terms: 18x + -18x = 0
40 + -18x + -1x2 = 0 + x2 + -1x2
40 + -18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + -18x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(20 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 0

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

Add '-20' to each side of the equation.
20 + -20 + x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x = 0 + -20
x = 0 + -20

Combine like terms: 0 + -20 = -20
x = -20

Simplifying
x = -20
Solution
x = {2, -20}