2(w-7)(-w+6)=0

Solution for 2(w-7)(-w+6)=0 equation:

Simplifying
2(w + -7)(-1w + 6) = 0

Reorder the terms:
2(-7 + w)(-1w + 6) = 0

Reorder the terms:
2(-7 + w)(6 + -1w) = 0

Multiply (-7 + w) * (6 + -1w)
2(-7(6 + -1w) + w(6 + -1w)) = 0
2((6 * -7 + -1w * -7) + w(6 + -1w)) = 0
2((-42 + 7w) + w(6 + -1w)) = 0
2(-42 + 7w + (6 * w + -1w * w)) = 0
2(-42 + 7w + (6w + -1w2)) = 0

Combine like terms: 7w + 6w = 13w
2(-42 + 13w + -1w2) = 0
(-42 * 2 + 13w * 2 + -1w2 * 2) = 0
(-84 + 26w + -2w2) = 0

Solving
-84 + 26w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 13w + -1w2) = 0

Factor a trinomial.
2((-7 + w)(6 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + w)' equal to zero and attempt to solve:

Simplifying
-7 + w = 0

Solving
-7 + w = 0

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

Add '7' to each side of the equation.
-7 + 7 + w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + w = 0 + 7
w = 0 + 7

Combine like terms: 0 + 7 = 7
w = 7

Simplifying
w = 7
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 = {7, 6}