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

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

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

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

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

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

Solving
2 + 2w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + w + -2w2) = 0

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

Ignore the factor 2.
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 '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 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 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {1, -0.5}