-9q^2+3q+6=0

Solution for -9q^2+3q+6=0 equation:

Simplifying
-9q2 + 3q + 6 = 0

Reorder the terms:
6 + 3q + -9q2 = 0

Solving
6 + 3q + -9q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + q + -3q2) = 0

Factor a trinomial.
3((1 + -1q)(2 + 3q)) = 0

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

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

Simplifying
2 + 3q = 0

Solving
2 + 3q = 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 + 3q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3q = 0 + -2
3q = 0 + -2

Combine like terms: 0 + -2 = -2
3q = -2

Divide each side by '3'.
q = -0.6666666667

Simplifying
q = -0.6666666667
Solution
q = {1, -0.6666666667}