6w^2-42w+72=0

Solution for 6w^2-42w+72=0 equation:

Simplifying
6w2 + -42w + 72 = 0

Reorder the terms:
72 + -42w + 6w2 = 0

Solving
72 + -42w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7w + w2) = 0

Factor a trinomial.
6((3 + -1w)(4 + -1w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

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

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

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {3, 4}