(w-8)*(w+5)=0

Solution for (w-8)*(w+5)=0 equation:

Simplifying
(w + -8)(w + 5) = 0

Reorder the terms:
(-8 + w)(w + 5) = 0

Reorder the terms:
(-8 + w)(5 + w) = 0

Multiply (-8 + w) * (5 + w)
(-8(5 + w) + w(5 + w)) = 0
((5 * -8 + w * -8) + w(5 + w)) = 0
((-40 + -8w) + w(5 + w)) = 0
(-40 + -8w + (5 * w + w * w)) = 0
(-40 + -8w + (5w + w2)) = 0

Combine like terms: -8w + 5w = -3w
(-40 + -3w + w2) = 0

Solving
-40 + -3w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -1w)(8 + -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 '(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
Solution
w = {-5, 8}