x(x+1)=3192

Solution for x(x+1)=3192 equation:

Simplifying
x(x + 1) = 3192

Reorder the terms:
x(1 + x) = 3192
(1 * x + x * x) = 3192
(1x + x2) = 3192

Solving
1x + x2 = 3192

Solving for variable 'x'.

Reorder the terms:
-3192 + 1x + x2 = 3192 + -3192

Combine like terms: 3192 + -3192 = 0
-3192 + 1x + x2 = 0

Factor a trinomial.
(-57 + -1x)(56 + -1x) = 0

Subproblem 1
Set the factor '(-57 + -1x)' equal to zero and attempt to solve:

Simplifying
-57 + -1x = 0

Solving
-57 + -1x = 0

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

Add '57' to each side of the equation.
-57 + 57 + -1x = 0 + 57

Combine like terms: -57 + 57 = 0
0 + -1x = 0 + 57
-1x = 0 + 57

Combine like terms: 0 + 57 = 57
-1x = 57

Divide each side by '-1'.
x = -57

Simplifying
x = -57
Subproblem 2
Set the factor '(56 + -1x)' equal to zero and attempt to solve:

Simplifying
56 + -1x = 0

Solving
56 + -1x = 0

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

Add '-56' to each side of the equation.
56 + -56 + -1x = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -1x = 0 + -56
-1x = 0 + -56

Combine like terms: 0 + -56 = -56
-1x = -56

Divide each side by '-1'.
x = 56

Simplifying
x = 56
Solution
x = {-57, 56}