(w+5)(w-12)=60

Solution for (w+5)(w-12)=60 equation:

Simplifying
(w + 5)(w + -12) = 60

Reorder the terms:
(5 + w)(w + -12) = 60

Reorder the terms:
(5 + w)(-12 + w) = 60

Multiply (5 + w) * (-12 + w)
(5(-12 + w) + w(-12 + w)) = 60
((-12 * 5 + w * 5) + w(-12 + w)) = 60
((-60 + 5w) + w(-12 + w)) = 60
(-60 + 5w + (-12 * w + w * w)) = 60
(-60 + 5w + (-12w + w2)) = 60

Combine like terms: 5w + -12w = -7w
(-60 + -7w + w2) = 60

Solving
-60 + -7w + w2 = 60

Solving for variable 'w'.

Reorder the terms:
-60 + -60 + -7w + w2 = 60 + -60

Combine like terms: -60 + -60 = -120
-120 + -7w + w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-120 + -7w + w2 = 0

Factor a trinomial.
(-8 + -1w)(15 + -1w) = 0

Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve:

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
w = -8

Simplifying
w = -8
Subproblem 2
Set the factor '(15 + -1w)' equal to zero and attempt to solve:

Simplifying
15 + -1w = 0

Solving
15 + -1w = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1w = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1w = 0 + -15
-1w = 0 + -15

Combine like terms: 0 + -15 = -15
-1w = -15

Divide each side by '-1'.
w = 15

Simplifying
w = 15
Solution
w = {-8, 15}