12k^2+54k+183=3-6k+7k^2

Solution for 12k^2+54k+183=3-6k+7k^2 equation:

Simplifying
12k2 + 54k + 183 = 3 + -6k + 7k2

Reorder the terms:
183 + 54k + 12k2 = 3 + -6k + 7k2

Solving
183 + 54k + 12k2 = 3 + -6k + 7k2

Solving for variable 'k'.

Reorder the terms:
183 + -3 + 54k + 6k + 12k2 + -7k2 = 3 + -6k + 7k2 + -3 + 6k + -7k2

Combine like terms: 183 + -3 = 180
180 + 54k + 6k + 12k2 + -7k2 = 3 + -6k + 7k2 + -3 + 6k + -7k2

Combine like terms: 54k + 6k = 60k
180 + 60k + 12k2 + -7k2 = 3 + -6k + 7k2 + -3 + 6k + -7k2

Combine like terms: 12k2 + -7k2 = 5k2
180 + 60k + 5k2 = 3 + -6k + 7k2 + -3 + 6k + -7k2

Reorder the terms:
180 + 60k + 5k2 = 3 + -3 + -6k + 6k + 7k2 + -7k2

Combine like terms: 3 + -3 = 0
180 + 60k + 5k2 = 0 + -6k + 6k + 7k2 + -7k2
180 + 60k + 5k2 = -6k + 6k + 7k2 + -7k2

Combine like terms: -6k + 6k = 0
180 + 60k + 5k2 = 0 + 7k2 + -7k2
180 + 60k + 5k2 = 7k2 + -7k2

Combine like terms: 7k2 + -7k2 = 0
180 + 60k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + 12k + k2) = 0

Factor a trinomial.
5((6 + k)(6 + k)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 0

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

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

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

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

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

Simplifying
6 + k = 0

Solving
6 + k = 0

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

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

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

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

Simplifying
k = -6
Solution
k = {-6, -6}