(5w+2)(4+w)=0

Solution for (5w+2)(4+w)=0 equation:

Simplifying
(5w + 2)(4 + w) = 0

Reorder the terms:
(2 + 5w)(4 + w) = 0

Multiply (2 + 5w) * (4 + w)
(2(4 + w) + 5w * (4 + w)) = 0
((4 * 2 + w * 2) + 5w * (4 + w)) = 0
((8 + 2w) + 5w * (4 + w)) = 0
(8 + 2w + (4 * 5w + w * 5w)) = 0
(8 + 2w + (20w + 5w2)) = 0

Combine like terms: 2w + 20w = 22w
(8 + 22w + 5w2) = 0

Solving
8 + 22w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + w)(2 + 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 '(2 + 5w)' equal to zero and attempt to solve:

Simplifying
2 + 5w = 0

Solving
2 + 5w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5w = 0 + -2
5w = 0 + -2

Combine like terms: 0 + -2 = -2
5w = -2

Divide each side by '5'.
w = -0.4

Simplifying
w = -0.4
Solution
w = {-4, -0.4}