(3+w)(4w+2)=0

Solution for (3+w)(4w+2)=0 equation:

Simplifying
(3 + w)(4w + 2) = 0

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

Multiply (3 + w) * (2 + 4w)
(3(2 + 4w) + w(2 + 4w)) = 0
((2 * 3 + 4w * 3) + w(2 + 4w)) = 0
((6 + 12w) + w(2 + 4w)) = 0
(6 + 12w + (2 * w + 4w * w)) = 0
(6 + 12w + (2w + 4w2)) = 0

Combine like terms: 12w + 2w = 14w
(6 + 14w + 4w2) = 0

Solving
6 + 14w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7w + 2w2) = 0

Factor a trinomial.
2((3 + w)(1 + 2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
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 = {-3, -0.5}