3q^2-27q+54=0

Solution for 3q^2-27q+54=0 equation:

Simplifying
3q2 + -27q + 54 = 0

Reorder the terms:
54 + -27q + 3q2 = 0

Solving
54 + -27q + 3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -9q + q2) = 0

Factor a trinomial.
3((3 + -1q)(6 + -1q)) = 0

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

Simplifying
3 + -1q = 0

Solving
3 + -1q = 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 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {3, 6}