(w-5)(w+3)=0

Solution for (w-5)(w+3)=0 equation:

Simplifying
(w + -5)(w + 3) = 0

Reorder the terms:
(-5 + w)(w + 3) = 0

Reorder the terms:
(-5 + w)(3 + w) = 0

Multiply (-5 + w) * (3 + w)
(-5(3 + w) + w(3 + w)) = 0
((3 * -5 + w * -5) + w(3 + w)) = 0
((-15 + -5w) + w(3 + w)) = 0
(-15 + -5w + (3 * w + w * w)) = 0
(-15 + -5w + (3w + w2)) = 0

Combine like terms: -5w + 3w = -2w
(-15 + -2w + w2) = 0

Solving
-15 + -2w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(5 + -1w) = 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 '(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
Solution
w = {-3, 5}