6q^4-8q^3+2q^2=0

Solution for 6q^4-8q^3+2q^2=0 equation:

Simplifying
6q4 + -8q3 + 2q2 = 0

Reorder the terms:
2q2 + -8q3 + 6q4 = 0

Solving
2q2 + -8q3 + 6q4 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q2'.
2q2(1 + -4q + 3q2) = 0

Factor a trinomial.
2q2((1 + -3q)(1 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve:

Simplifying
q2 = 0

Solving
q2 = 0

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

Simplifying
q2 = 0

Take the square root of each side:
q = {0}
Subproblem 2
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
Subproblem 3
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
Solution
q = {0, 0.3333333333, 1}