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

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

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

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

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

Combine like terms: 1w + 16w = 17w
(4 + 17w + 4w2) = 0

Solving
4 + 17w + 4w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

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

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

Combine like terms: 0 + -4 = -4
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}