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

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

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

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

Multiply (-2 + 4w) * (4 + w)
(-2(4 + w) + 4w * (4 + w)) = 0
((4 * -2 + w * -2) + 4w * (4 + w)) = 0
((-8 + -2w) + 4w * (4 + w)) = 0
(-8 + -2w + (4 * 4w + w * 4w)) = 0
(-8 + -2w + (16w + 4w2)) = 0

Combine like terms: -2w + 16w = 14w
(-8 + 14w + 4w2) = 0

Solving
-8 + 14w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 7w + 2w2) = 0

Factor a trinomial.
2((-4 + -1w)(1 + -2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
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 = {-4, 0.5}