(w+5)(w-4)=-8

Solution for (w+5)(w-4)=-8 equation:

Simplifying
(w + 5)(w + -4) = -8

Reorder the terms:
(5 + w)(w + -4) = -8

Reorder the terms:
(5 + w)(-4 + w) = -8

Multiply (5 + w) * (-4 + w)
(5(-4 + w) + w(-4 + w)) = -8
((-4 * 5 + w * 5) + w(-4 + w)) = -8
((-20 + 5w) + w(-4 + w)) = -8
(-20 + 5w + (-4 * w + w * w)) = -8
(-20 + 5w + (-4w + w2)) = -8

Combine like terms: 5w + -4w = 1w
(-20 + 1w + w2) = -8

Solving
-20 + 1w + w2 = -8

Solving for variable 'w'.

Reorder the terms:
-20 + 8 + 1w + w2 = -8 + 8

Combine like terms: -20 + 8 = -12
-12 + 1w + w2 = -8 + 8

Combine like terms: -8 + 8 = 0
-12 + 1w + w2 = 0

Factor a trinomial.
(-4 + -1w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
Subproblem 2
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
Solution
w = {-4, 3}