x(x+1)=2652

Solution for x(x+1)=2652 equation:

Simplifying
x(x + 1) = 2652

Reorder the terms:
x(1 + x) = 2652
(1 * x + x * x) = 2652
(1x + x2) = 2652

Solving
1x + x2 = 2652

Solving for variable 'x'.

Reorder the terms:
-2652 + 1x + x2 = 2652 + -2652

Combine like terms: 2652 + -2652 = 0
-2652 + 1x + x2 = 0

Factor a trinomial.
(-52 + -1x)(51 + -1x) = 0

Subproblem 1
Set the factor '(-52 + -1x)' equal to zero and attempt to solve:

Simplifying
-52 + -1x = 0

Solving
-52 + -1x = 0

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

Add '52' to each side of the equation.
-52 + 52 + -1x = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -1x = 0 + 52
-1x = 0 + 52

Combine like terms: 0 + 52 = 52
-1x = 52

Divide each side by '-1'.
x = -52

Simplifying
x = -52
Subproblem 2
Set the factor '(51 + -1x)' equal to zero and attempt to solve:

Simplifying
51 + -1x = 0

Solving
51 + -1x = 0

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

Add '-51' to each side of the equation.
51 + -51 + -1x = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -1x = 0 + -51
-1x = 0 + -51

Combine like terms: 0 + -51 = -51
-1x = -51

Divide each side by '-1'.
x = 51

Simplifying
x = 51
Solution
x = {-52, 51}