c^2+18c+54=-23

Solution for c^2+18c+54=-23 equation:

Simplifying
c2 + 18c + 54 = -23

Reorder the terms:
54 + 18c + c2 = -23

Solving
54 + 18c + c2 = -23

Solving for variable 'c'.

Reorder the terms:
54 + 23 + 18c + c2 = -23 + 23

Combine like terms: 54 + 23 = 77
77 + 18c + c2 = -23 + 23

Combine like terms: -23 + 23 = 0
77 + 18c + c2 = 0

Factor a trinomial.
(11 + c)(7 + c) = 0

Subproblem 1
Set the factor '(11 + c)' equal to zero and attempt to solve:

Simplifying
11 + c = 0

Solving
11 + c = 0

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

Add '-11' to each side of the equation.
11 + -11 + c = 0 + -11

Combine like terms: 11 + -11 = 0
0 + c = 0 + -11
c = 0 + -11

Combine like terms: 0 + -11 = -11
c = -11

Simplifying
c = -11
Subproblem 2
Set the factor '(7 + c)' equal to zero and attempt to solve:

Simplifying
7 + c = 0

Solving
7 + c = 0

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

Add '-7' to each side of the equation.
7 + -7 + c = 0 + -7

Combine like terms: 7 + -7 = 0
0 + c = 0 + -7
c = 0 + -7

Combine like terms: 0 + -7 = -7
c = -7

Simplifying
c = -7
Solution
c = {-11, -7}