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

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

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

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

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