X(X+15)=-54

Solution for X(X+15)=-54 equation:

Simplifying
X(X + 15) = -54

Reorder the terms:
X(15 + X) = -54
(15 * X + X * X) = -54
(15X + X2) = -54

Solving
15X + X2 = -54

Solving for variable 'X'.

Reorder the terms:
54 + 15X + X2 = -54 + 54

Combine like terms: -54 + 54 = 0
54 + 15X + X2 = 0

Factor a trinomial.
(9 + X)(6 + X) = 0

Subproblem 1
Set the factor '(9 + X)' equal to zero and attempt to solve:

Simplifying
9 + X = 0

Solving
9 + X = 0

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

Add '-9' to each side of the equation.
9 + -9 + X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + X = 0 + -9
X = 0 + -9

Combine like terms: 0 + -9 = -9
X = -9

Simplifying
X = -9
Subproblem 2
Set the factor '(6 + X)' equal to zero and attempt to solve:

Simplifying
6 + X = 0

Solving
6 + X = 0

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

Add '-6' to each side of the equation.
6 + -6 + X = 0 + -6

Combine like terms: 6 + -6 = 0
0 + X = 0 + -6
X = 0 + -6

Combine like terms: 0 + -6 = -6
X = -6

Simplifying
X = -6
Solution
X = {-9, -6}