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

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

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

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

Multiply (2 + 4w) * (2 + -1w)
(2(2 + -1w) + 4w * (2 + -1w)) = 0
((2 * 2 + -1w * 2) + 4w * (2 + -1w)) = 0
((4 + -2w) + 4w * (2 + -1w)) = 0
(4 + -2w + (2 * 4w + -1w * 4w)) = 0
(4 + -2w + (8w + -4w2)) = 0

Combine like terms: -2w + 8w = 6w
(4 + 6w + -4w2) = 0

Solving
4 + 6w + -4w2 = 0

Solving for variable 'w'.

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

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

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
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 = {2, -0.5}