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

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

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

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

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

Combine like terms: 5w + 4w = 9w
(4 + 9w + 5w2) = 0

Solving
4 + 9w + 5w2 = 0

Solving for variable 'w'.

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

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

Simplifying
1 + w = 0

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

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

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

Simplifying
w = -1
Subproblem 2
Set the factor '(4 + 5w)' equal to zero and attempt to solve:

Simplifying
4 + 5w = 0

Solving
4 + 5w = 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 + 5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5w = 0 + -4
5w = 0 + -4

Combine like terms: 0 + -4 = -4
5w = -4

Divide each side by '5'.
w = -0.8

Simplifying
w = -0.8
Solution
w = {-1, -0.8}