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

Solution for (2-w)(4w-1)=0 equation:

Simplifying
(2 + -1w)(4w + -1) = 0

Reorder the terms:
(2 + -1w)(-1 + 4w) = 0

Multiply (2 + -1w) * (-1 + 4w)
(2(-1 + 4w) + -1w * (-1 + 4w)) = 0
((-1 * 2 + 4w * 2) + -1w * (-1 + 4w)) = 0
((-2 + 8w) + -1w * (-1 + 4w)) = 0
(-2 + 8w + (-1 * -1w + 4w * -1w)) = 0
(-2 + 8w + (1w + -4w2)) = 0

Combine like terms: 8w + 1w = 9w
(-2 + 9w + -4w2) = 0

Solving
-2 + 9w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-2 + w)(1 + -4w) = 0

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

Simplifying
-2 + w = 0

Solving
-2 + w = 0

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

Add '2' to each side of the equation.
-2 + 2 + w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + w = 0 + 2
w = 0 + 2

Combine like terms: 0 + 2 = 2
w = 2

Simplifying
w = 2
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 = {2, 0.25}