3w^2-12w+12=0

Solution for 3w^2-12w+12=0 equation:

Simplifying
3w2 + -12w + 12 = 0

Reorder the terms:
12 + -12w + 3w2 = 0

Solving
12 + -12w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4w + w2) = 0

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

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

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

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

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

Simplifying
w = 2
Solution
w = {2, 2}