72=(6+w)(5+w)

Solution for 72=(6+w)(5+w) equation:

Simplifying
72 = (6 + w)(5 + w)

Multiply (6 + w) * (5 + w)
72 = (6(5 + w) + w(5 + w))
72 = ((5 * 6 + w * 6) + w(5 + w))
72 = ((30 + 6w) + w(5 + w))
72 = (30 + 6w + (5 * w + w * w))
72 = (30 + 6w + (5w + w2))

Combine like terms: 6w + 5w = 11w
72 = (30 + 11w + w2)

Solving
72 = 30 + 11w + w2

Solving for variable 'w'.

Combine like terms: 72 + -30 = 42
42 + -11w + -1w2 = 30 + 11w + w2 + -30 + -11w + -1w2

Reorder the terms:
42 + -11w + -1w2 = 30 + -30 + 11w + -11w + w2 + -1w2

Combine like terms: 30 + -30 = 0
42 + -11w + -1w2 = 0 + 11w + -11w + w2 + -1w2
42 + -11w + -1w2 = 11w + -11w + w2 + -1w2

Combine like terms: 11w + -11w = 0
42 + -11w + -1w2 = 0 + w2 + -1w2
42 + -11w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
42 + -11w + -1w2 = 0

Factor a trinomial.
(3 + -1w)(14 + w) = 0

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 '(14 + w)' equal to zero and attempt to solve:

Simplifying
14 + w = 0

Solving
14 + w = 0

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

Add '-14' to each side of the equation.
14 + -14 + w = 0 + -14

Combine like terms: 14 + -14 = 0
0 + w = 0 + -14
w = 0 + -14

Combine like terms: 0 + -14 = -14
w = -14

Simplifying
w = -14
Solution
w = {3, -14}