118-2x=x^2-18x+82

Solution for 118-2x=x^2-18x+82 equation:

Simplifying
118 + -2x = x2 + -18x + 82

Reorder the terms:
118 + -2x = 82 + -18x + x2

Solving
118 + -2x = 82 + -18x + x2

Solving for variable 'x'.

Reorder the terms:
118 + -82 + -2x + 18x + -1x2 = 82 + -18x + x2 + -82 + 18x + -1x2

Combine like terms: 118 + -82 = 36
36 + -2x + 18x + -1x2 = 82 + -18x + x2 + -82 + 18x + -1x2

Combine like terms: -2x + 18x = 16x
36 + 16x + -1x2 = 82 + -18x + x2 + -82 + 18x + -1x2

Reorder the terms:
36 + 16x + -1x2 = 82 + -82 + -18x + 18x + x2 + -1x2

Combine like terms: 82 + -82 = 0
36 + 16x + -1x2 = 0 + -18x + 18x + x2 + -1x2
36 + 16x + -1x2 = -18x + 18x + x2 + -1x2

Combine like terms: -18x + 18x = 0
36 + 16x + -1x2 = 0 + x2 + -1x2
36 + 16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + 16x + -1x2 = 0

Factor a trinomial.
(18 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

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

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

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {18, -2}