7w^2-84w+252=0

Solution for 7w^2-84w+252=0 equation:

Simplifying
7w2 + -84w + 252 = 0

Reorder the terms:
252 + -84w + 7w2 = 0

Solving
252 + -84w + 7w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '7'.
7(36 + -12w + w2) = 0

Factor a trinomial.
7((6 + -1w)(6 + -1w)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {6, 6}