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

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

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

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

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

Combine like terms: -1w + 8w = 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}