x(x+1)=29+x+x+1

Solution for x(x+1)=29+x+x+1 equation:

Simplifying
x(x + 1) = 29 + x + x + 1

Reorder the terms:
x(1 + x) = 29 + x + x + 1
(1 * x + x * x) = 29 + x + x + 1
(1x + x2) = 29 + x + x + 1

Reorder the terms:
1x + x2 = 29 + 1 + x + x

Combine like terms: 29 + 1 = 30
1x + x2 = 30 + x + x

Combine like terms: x + x = 2x
1x + x2 = 30 + 2x

Solving
1x + x2 = 30 + 2x

Solving for variable 'x'.

Reorder the terms:
-30 + 1x + -2x + x2 = 30 + 2x + -30 + -2x

Combine like terms: 1x + -2x = -1x
-30 + -1x + x2 = 30 + 2x + -30 + -2x

Reorder the terms:
-30 + -1x + x2 = 30 + -30 + 2x + -2x

Combine like terms: 30 + -30 = 0
-30 + -1x + x2 = 0 + 2x + -2x
-30 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-30 + -1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-5, 6}