72=(w+11)(2)(w-5)

Solution for 72=(w+11)(2)(w-5) equation:

Simplifying
72 = (w + 11)(2)(w + -5)

Reorder the terms:
72 = (11 + w)(2)(w + -5)

Reorder the terms:
72 = (11 + w) * 2(-5 + w)

Reorder the terms for easier multiplication:
72 = 2(11 + w)(-5 + w)

Multiply (11 + w) * (-5 + w)
72 = 2(11(-5 + w) + w(-5 + w))
72 = 2((-5 * 11 + w * 11) + w(-5 + w))
72 = 2((-55 + 11w) + w(-5 + w))
72 = 2(-55 + 11w + (-5 * w + w * w))
72 = 2(-55 + 11w + (-5w + w2))

Combine like terms: 11w + -5w = 6w
72 = 2(-55 + 6w + w2)
72 = (-55 * 2 + 6w * 2 + w2 * 2)
72 = (-110 + 12w + 2w2)

Solving
72 = -110 + 12w + 2w2

Solving for variable 'w'.

Combine like terms: 72 + 110 = 182
182 + -12w + -2w2 = -110 + 12w + 2w2 + 110 + -12w + -2w2

Reorder the terms:
182 + -12w + -2w2 = -110 + 110 + 12w + -12w + 2w2 + -2w2

Combine like terms: -110 + 110 = 0
182 + -12w + -2w2 = 0 + 12w + -12w + 2w2 + -2w2
182 + -12w + -2w2 = 12w + -12w + 2w2 + -2w2

Combine like terms: 12w + -12w = 0
182 + -12w + -2w2 = 0 + 2w2 + -2w2
182 + -12w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
182 + -12w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(91 + -6w + -1w2) = 0

Factor a trinomial.
2((7 + -1w)(13 + w)) = 0

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

Simplifying
7 + -1w = 0

Solving
7 + -1w = 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 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Subproblem 2
Set the factor '(13 + w)' equal to zero and attempt to solve:

Simplifying
13 + w = 0

Solving
13 + w = 0

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

Add '-13' to each side of the equation.
13 + -13 + w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + w = 0 + -13
w = 0 + -13

Combine like terms: 0 + -13 = -13
w = -13

Simplifying
w = -13
Solution
w = {7, -13}