3q(q-4)=-9

Solution for 3q(q-4)=-9 equation:

Simplifying
3q(q + -4) = -9

Reorder the terms:
3q(-4 + q) = -9
(-4 * 3q + q * 3q) = -9
(-12q + 3q2) = -9

Solving
-12q + 3q2 = -9

Solving for variable 'q'.

Reorder the terms:
9 + -12q + 3q2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -12q + 3q2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -4q + 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}