x(x+1)=992

Solution for x(x+1)=992 equation:

Simplifying
x(x + 1) = 992

Reorder the terms:
x(1 + x) = 992
(1 * x + x * x) = 992
(1x + x2) = 992

Solving
1x + x2 = 992

Solving for variable 'x'.

Reorder the terms:
-992 + 1x + x2 = 992 + -992

Combine like terms: 992 + -992 = 0
-992 + 1x + x2 = 0

Factor a trinomial.
(-32 + -1x)(31 + -1x) = 0

Subproblem 1
Set the factor '(-32 + -1x)' equal to zero and attempt to solve:

Simplifying
-32 + -1x = 0

Solving
-32 + -1x = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1x = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1x = 0 + 32
-1x = 0 + 32

Combine like terms: 0 + 32 = 32
-1x = 32

Divide each side by '-1'.
x = -32

Simplifying
x = -32
Subproblem 2
Set the factor '(31 + -1x)' equal to zero and attempt to solve:

Simplifying
31 + -1x = 0

Solving
31 + -1x = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1x = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1x = 0 + -31
-1x = 0 + -31

Combine like terms: 0 + -31 = -31
-1x = -31

Divide each side by '-1'.
x = 31

Simplifying
x = 31
Solution
x = {-32, 31}