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

Solution for (1+w)(5w-4)=0 equation:

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

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

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

Combine like terms: 5w + -4w = 1w
(-4 + 1w + 5w2) = 0

Solving
-4 + 1w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(4 + -5w) = 0

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

Simplifying
w = -1
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 = {-1, 0.8}