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

Solution for (5+w)(4w+1)=0 equation:

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

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

Multiply (5 + w) * (1 + 4w)
(5(1 + 4w) + w(1 + 4w)) = 0
((1 * 5 + 4w * 5) + w(1 + 4w)) = 0
((5 + 20w) + w(1 + 4w)) = 0
(5 + 20w + (1 * w + 4w * w)) = 0
(5 + 20w + (1w + 4w2)) = 0

Combine like terms: 20w + 1w = 21w
(5 + 21w + 4w2) = 0

Solving
5 + 21w + 4w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
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 = {-5, -0.25}