-x^2-22x=112

Solution for -x^2-22x=112 equation:

Simplifying
-1x2 + -22x = 112

Reorder the terms:
-22x + -1x2 = 112

Solving
-22x + -1x2 = 112

Solving for variable 'x'.

Reorder the terms:
-112 + -22x + -1x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + -22x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(112 + 22x + x2) = 0

Factor a trinomial.
-1((14 + x)(8 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-14, -8}