3q^2-6q+3=0

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

Simplifying
3q2 + -6q + 3 = 0

Reorder the terms:
3 + -6q + 3q2 = 0

Solving
3 + -6q + 3q2 = 0

Solving for variable 'q'.

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

Factor a trinomial.
3((1 + -1q)(1 + -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 '(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 = {1, 1}