3q(q-2)=9

Solution for 3q(q-2)=9 equation:

Simplifying
3q(q + -2) = 9

Reorder the terms:
3q(-2 + q) = 9
(-2 * 3q + q * 3q) = 9
(-6q + 3q2) = 9

Solving
-6q + 3q2 = 9

Solving for variable 'q'.

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

Combine like terms: 9 + -9 = 0
-9 + -6q + 3q2 = 0

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

Factor a trinomial.
3((-1 + -1q)(3 + -1q)) = 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 '(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
Solution
q = {-1, 3}