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

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

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

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

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

Remove parenthesis around (1 + x)
1x + x2 = 29 + -1x + 1 + x

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

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

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

Solving
1x + x2 = 30

Solving for variable 'x'.

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

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

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

Subproblem 1
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
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 = {-6, 5}