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

Solution for (4w+2)(6+w)=0 equation:

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

Reorder the terms:
(2 + 4w)(6 + w) = 0

Multiply (2 + 4w) * (6 + w)
(2(6 + w) + 4w * (6 + w)) = 0
((6 * 2 + w * 2) + 4w * (6 + w)) = 0
((12 + 2w) + 4w * (6 + w)) = 0
(12 + 2w + (6 * 4w + w * 4w)) = 0
(12 + 2w + (24w + 4w2)) = 0

Combine like terms: 2w + 24w = 26w
(12 + 26w + 4w2) = 0

Solving
12 + 26w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 13w + 2w2) = 0

Factor a trinomial.
2((6 + w)(1 + 2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
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 = {-6, -0.5}