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

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

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

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

Multiply (4 + -1w) * (1 + 4w)
(4(1 + 4w) + -1w * (1 + 4w)) = 0
((1 * 4 + 4w * 4) + -1w * (1 + 4w)) = 0
((4 + 16w) + -1w * (1 + 4w)) = 0
(4 + 16w + (1 * -1w + 4w * -1w)) = 0
(4 + 16w + (-1w + -4w2)) = 0

Combine like terms: 16w + -1w = 15w
(4 + 15w + -4w2) = 0

Solving
4 + 15w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + -1w)(1 + 4w) = 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 + 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 = {4, -0.25}