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

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

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

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

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