x*(x+1)=240

Solution for x*(x+1)=240 equation:

Simplifying
x(x + 1) = 240

Reorder the terms:
x(1 + x) = 240
(1 * x + x * x) = 240
(1x + x2) = 240

Solving
1x + x2 = 240

Solving for variable 'x'.

Reorder the terms:
-240 + 1x + x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 1x + x2 = 0

Factor a trinomial.
(-16 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-16, 15}