(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 = 6w
(2 + 6w + 4w2) = 0

Solving
2 + 6w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3w + 2w2) = 0

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

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

Simplifying
1 + w = 0

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

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

Combine like terms: 0 + -1 = -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}