x(x+1)=182

Solution for x(x+1)=182 equation:

Simplifying
x(x + 1) = 182

Reorder the terms:
x(1 + x) = 182
(1 * x + x * x) = 182
(1x + x2) = 182

Solving
1x + x2 = 182

Solving for variable 'x'.

Reorder the terms:
-182 + 1x + x2 = 182 + -182

Combine like terms: 182 + -182 = 0
-182 + 1x + x2 = 0

Factor a trinomial.
(-14 + -1x)(13 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
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
Solution
x = {-14, 13}