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

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

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

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

Multiply (2 + w) * (4 + 5w)
(2(4 + 5w) + w(4 + 5w)) = 0
((4 * 2 + 5w * 2) + w(4 + 5w)) = 0
((8 + 10w) + w(4 + 5w)) = 0
(8 + 10w + (4 * w + 5w * w)) = 0
(8 + 10w + (4w + 5w2)) = 0

Combine like terms: 10w + 4w = 14w
(8 + 14w + 5w2) = 0

Solving
8 + 14w + 5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

Simplifying
w = -2
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 = {-2, -0.8}