3q^2+27q+18=12q

Solution for 3q^2+27q+18=12q equation:

Simplifying
3q2 + 27q + 18 = 12q

Reorder the terms:
18 + 27q + 3q2 = 12q

Solving
18 + 27q + 3q2 = 12q

Solving for variable 'q'.

Reorder the terms:
18 + 27q + -12q + 3q2 = 12q + -12q

Combine like terms: 27q + -12q = 15q
18 + 15q + 3q2 = 12q + -12q

Combine like terms: 12q + -12q = 0
18 + 15q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 5q + q2) = 0

Factor a trinomial.
3((3 + q)(2 + q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 0

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

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

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

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

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

Simplifying
2 + q = 0

Solving
2 + q = 0

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

Add '-2' to each side of the equation.
2 + -2 + q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + q = 0 + -2
q = 0 + -2

Combine like terms: 0 + -2 = -2
q = -2

Simplifying
q = -2
Solution
q = {-3, -2}