x(x+1)-11(x+1)=0

Solution for x(x+1)-11(x+1)=0 equation:

Simplifying
x(x + 1) + -11(x + 1) = 0

Reorder the terms:
x(1 + x) + -11(x + 1) = 0
(1 * x + x * x) + -11(x + 1) = 0
(1x + x2) + -11(x + 1) = 0

Reorder the terms:
1x + x2 + -11(1 + x) = 0
1x + x2 + (1 * -11 + x * -11) = 0
1x + x2 + (-11 + -11x) = 0

Reorder the terms:
-11 + 1x + -11x + x2 = 0

Combine like terms: 1x + -11x = -10x
-11 + -10x + x2 = 0

Solving
-11 + -10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(11 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 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 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-1, 11}