x(x+1)=x+x+1+11

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

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

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

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

Combine like terms: 1 + 11 = 12
1x + x2 = 12 + x + x

Combine like terms: x + x = 2x
1x + x2 = 12 + 2x

Solving
1x + x2 = 12 + 2x

Solving for variable 'x'.

Reorder the terms:
-12 + 1x + -2x + x2 = 12 + 2x + -12 + -2x

Combine like terms: 1x + -2x = -1x
-12 + -1x + x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-12 + -1x + x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-12 + -1x + x2 = 0 + 2x + -2x
-12 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}