(w+5)(w-12)=0

Solution for (w+5)(w-12)=0 equation:

Simplifying
(w + 5)(w + -12) = 0

Reorder the terms:
(5 + w)(w + -12) = 0

Reorder the terms:
(5 + w)(-12 + w) = 0

Multiply (5 + w) * (-12 + w)
(5(-12 + w) + w(-12 + w)) = 0
((-12 * 5 + w * 5) + w(-12 + w)) = 0
((-60 + 5w) + w(-12 + w)) = 0
(-60 + 5w + (-12 * w + w * w)) = 0
(-60 + 5w + (-12w + w2)) = 0

Combine like terms: 5w + -12w = -7w
(-60 + -7w + w2) = 0

Solving
-60 + -7w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -1w)(12 + -1w) = 0

Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve:

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {-5, 12}