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

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

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

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

Multiply (5 + -1w) * (-1 + 4w)
(5(-1 + 4w) + -1w * (-1 + 4w)) = 0
((-1 * 5 + 4w * 5) + -1w * (-1 + 4w)) = 0
((-5 + 20w) + -1w * (-1 + 4w)) = 0
(-5 + 20w + (-1 * -1w + 4w * -1w)) = 0
(-5 + 20w + (1w + -4w2)) = 0

Combine like terms: 20w + 1w = 21w
(-5 + 21w + -4w2) = 0

Solving
-5 + 21w + -4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-5 + w = 0

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

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

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

Simplifying
w = 5
Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 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 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {5, 0.25}