240=X(X+1)

Solution for 240=X(X+1) equation:

Simplifying
240 = X(X + 1)

Reorder the terms:
240 = X(1 + X)
240 = (1 * X + X * X)
240 = (1X + X2)

Solving
240 = 1X + X2

Solving for variable 'X'.

Reorder the terms:
240 + -1X + -1X2 = 1X + -1X + X2 + -1X2

Combine like terms: 1X + -1X = 0
240 + -1X + -1X2 = 0 + X2 + -1X2
240 + -1X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
240 + -1X + -1X2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(16 + X)' equal to zero and attempt to solve:

Simplifying
16 + X = 0

Solving
16 + X = 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 + X = 0 + -16

Combine like terms: 16 + -16 = 0
0 + X = 0 + -16
X = 0 + -16

Combine like terms: 0 + -16 = -16
X = -16

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