6q^2-9q=0

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

Simplifying
6q2 + -9q = 0

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

Solving
-9q + 6q2 = 0

Solving for variable 'q'.

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

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

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(-3 + 2q)' equal to zero and attempt to solve:

Simplifying
-3 + 2q = 0

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

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

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

Divide each side by '2'.
q = 1.5

Simplifying
q = 1.5
Solution
q = {0, 1.5}