(8-w)(5w-4)=0

Solution for (8-w)(5w-4)=0 equation:

Simplifying
(8 + -1w)(5w + -4) = 0

Reorder the terms:
(8 + -1w)(-4 + 5w) = 0

Multiply (8 + -1w) * (-4 + 5w)
(8(-4 + 5w) + -1w * (-4 + 5w)) = 0
((-4 * 8 + 5w * 8) + -1w * (-4 + 5w)) = 0
((-32 + 40w) + -1w * (-4 + 5w)) = 0
(-32 + 40w + (-4 * -1w + 5w * -1w)) = 0
(-32 + 40w + (4w + -5w2)) = 0

Combine like terms: 40w + 4w = 44w
(-32 + 44w + -5w2) = 0

Solving
-32 + 44w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + w)(4 + -5w) = 0

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

Simplifying
-8 + w = 0

Solving
-8 + w = 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 + w = 0 + 8

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

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

Simplifying
w = 8
Subproblem 2
Set the factor '(4 + -5w)' equal to zero and attempt to solve:

Simplifying
4 + -5w = 0

Solving
4 + -5w = 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 + -5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5w = 0 + -4
-5w = 0 + -4

Combine like terms: 0 + -4 = -4
-5w = -4

Divide each side by '-5'.
w = 0.8

Simplifying
w = 0.8
Solution
w = {8, 0.8}