x(x+1)=11(x+x+1)+35

Solution for x(x+1)=11(x+x+1)+35 equation:

Simplifying
x(x + 1) = 11(x + x + 1) + 35

Reorder the terms:
x(1 + x) = 11(x + x + 1) + 35
(1 * x + x * x) = 11(x + x + 1) + 35
(1x + x2) = 11(x + x + 1) + 35

Reorder the terms:
1x + x2 = 11(1 + x + x) + 35

Combine like terms: x + x = 2x
1x + x2 = 11(1 + 2x) + 35
1x + x2 = (1 * 11 + 2x * 11) + 35
1x + x2 = (11 + 22x) + 35

Reorder the terms:
1x + x2 = 11 + 35 + 22x

Combine like terms: 11 + 35 = 46
1x + x2 = 46 + 22x

Solving
1x + x2 = 46 + 22x

Solving for variable 'x'.

Reorder the terms:
-46 + 1x + -22x + x2 = 46 + 22x + -46 + -22x

Combine like terms: 1x + -22x = -21x
-46 + -21x + x2 = 46 + 22x + -46 + -22x

Reorder the terms:
-46 + -21x + x2 = 46 + -46 + 22x + -22x

Combine like terms: 46 + -46 = 0
-46 + -21x + x2 = 0 + 22x + -22x
-46 + -21x + x2 = 22x + -22x

Combine like terms: 22x + -22x = 0
-46 + -21x + x2 = 0

Factor a trinomial.
(-2 + -1x)(23 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Solution
x = {-2, 23}