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

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

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

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

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

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

Solving
-2 + 7w + 4w2 = 0

Solving for variable 'w'.

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

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 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 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 + -4w = 0 + -1

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

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

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {-2, 0.25}