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

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

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

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

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