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

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

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

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

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

Combine like terms: 4w + 5w = 9w
(-5 + 9w + -4w2) = 0

Solving
-5 + 9w + -4w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-5 + 4w)' equal to zero and attempt to solve:

Simplifying
-5 + 4w = 0

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

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

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

Divide each side by '4'.
w = 1.25

Simplifying
w = 1.25
Subproblem 2
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
Solution
w = {1.25, 1}