x^2-11x-11=-9x+4

Solution for x^2-11x-11=-9x+4 equation:

Simplifying
x2 + -11x + -11 = -9x + 4

Reorder the terms:
-11 + -11x + x2 = -9x + 4

Reorder the terms:
-11 + -11x + x2 = 4 + -9x

Solving
-11 + -11x + x2 = 4 + -9x

Solving for variable 'x'.

Reorder the terms:
-11 + -4 + -11x + 9x + x2 = 4 + -9x + -4 + 9x

Combine like terms: -11 + -4 = -15
-15 + -11x + 9x + x2 = 4 + -9x + -4 + 9x

Combine like terms: -11x + 9x = -2x
-15 + -2x + x2 = 4 + -9x + -4 + 9x

Reorder the terms:
-15 + -2x + x2 = 4 + -4 + -9x + 9x

Combine like terms: 4 + -4 = 0
-15 + -2x + x2 = 0 + -9x + 9x
-15 + -2x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}