6q^3+34q^2-12q=0

Solution for 6q^3+34q^2-12q=0 equation:

Simplifying
6q3 + 34q2 + -12q = 0

Reorder the terms:
-12q + 34q2 + 6q3 = 0

Solving
-12q + 34q2 + 6q3 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q'.
2q(-6 + 17q + 3q2) = 0

Factor a trinomial.
2q((-6 + -1q)(1 + -3q)) = 0

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

Simplifying
1 + -3q = 0

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

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

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

Divide each side by '-3'.
q = 0.3333333333

Simplifying
q = 0.3333333333
Solution
q = {0, -6, 0.3333333333}