X^2+21X=-54

Solution for X^2+21X=-54 equation:

Simplifying
X2 + 21X = -54

Reorder the terms:
21X + X2 = -54

Solving
21X + X2 = -54

Solving for variable 'X'.

Reorder the terms:
54 + 21X + X2 = -54 + 54

Combine like terms: -54 + 54 = 0
54 + 21X + X2 = 0

Factor a trinomial.
(18 + X)(3 + X) = 0

Subproblem 1
Set the factor '(18 + X)' equal to zero and attempt to solve:

Simplifying
18 + X = 0

Solving
18 + X = 0

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

Add '-18' to each side of the equation.
18 + -18 + X = 0 + -18

Combine like terms: 18 + -18 = 0
0 + X = 0 + -18
X = 0 + -18

Combine like terms: 0 + -18 = -18
X = -18

Simplifying
X = -18
Subproblem 2
Set the factor '(3 + X)' equal to zero and attempt to solve:

Simplifying
3 + X = 0

Solving
3 + X = 0

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

Add '-3' to each side of the equation.
3 + -3 + X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + X = 0 + -3
X = 0 + -3

Combine like terms: 0 + -3 = -3
X = -3

Simplifying
X = -3
Solution
X = {-18, -3}