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

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

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

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

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

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

Solving
4 + 21w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + w)(1 + 5w) = 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 + 5w)' equal to zero and attempt to solve:

Simplifying
1 + 5w = 0

Solving
1 + 5w = 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 + 5w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5w = 0 + -1
5w = 0 + -1

Combine like terms: 0 + -1 = -1
5w = -1

Divide each side by '5'.
w = -0.2

Simplifying
w = -0.2
Solution
w = {-4, -0.2}