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

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

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

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

Multiply (5 + w) * (-4 + 5w)
(5(-4 + 5w) + w(-4 + 5w)) = 0
((-4 * 5 + 5w * 5) + w(-4 + 5w)) = 0
((-20 + 25w) + w(-4 + 5w)) = 0
(-20 + 25w + (-4 * w + 5w * w)) = 0
(-20 + 25w + (-4w + 5w2)) = 0

Combine like terms: 25w + -4w = 21w
(-20 + 21w + 5w2) = 0

Solving
-20 + 21w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -1w)(4 + -5w) = 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 '(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 = {-5, 0.8}