x(x+1)=156

Solution for x(x+1)=156 equation:

Simplifying
x(x + 1) = 156

Reorder the terms:
x(1 + x) = 156
(1 * x + x * x) = 156
(1x + x2) = 156

Solving
1x + x2 = 156

Solving for variable 'x'.

Reorder the terms:
-156 + 1x + x2 = 156 + -156

Combine like terms: 156 + -156 = 0
-156 + 1x + x2 = 0

Factor a trinomial.
(-13 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-13, 12}