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

Solution for (4-w)(2w+1)=0 equation:

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

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

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

Combine like terms: 8w + -1w = 7w
(4 + 7w + -2w2) = 0

Solving
4 + 7w + -2w2 = 0

Solving for variable 'w'.

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

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}