8q^4-22q^3+12q^2=0

Solution for 8q^4-22q^3+12q^2=0 equation:

Simplifying
8q4 + -22q3 + 12q2 = 0

Reorder the terms:
12q2 + -22q3 + 8q4 = 0

Solving
12q2 + -22q3 + 8q4 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2q2'.
2q2(6 + -11q + 4q2) = 0

Factor a trinomial.
2q2((3 + -4q)(2 + -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 '(3 + -4q)' equal to zero and attempt to solve:

Simplifying
3 + -4q = 0

Solving
3 + -4q = 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 + -4q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4q = 0 + -3
-4q = 0 + -3

Combine like terms: 0 + -3 = -3
-4q = -3

Divide each side by '-4'.
q = 0.75

Simplifying
q = 0.75
Subproblem 3
Set the factor '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Solution
q = {0, 0.75, 2}