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

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

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

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

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