(5w+9)(5+w)=0

Solution for (5w+9)(5+w)=0 equation:

Simplifying
(5w + 9)(5 + w) = 0

Reorder the terms:
(9 + 5w)(5 + w) = 0

Multiply (9 + 5w) * (5 + w)
(9(5 + w) + 5w * (5 + w)) = 0
((5 * 9 + w * 9) + 5w * (5 + w)) = 0
((45 + 9w) + 5w * (5 + w)) = 0
(45 + 9w + (5 * 5w + w * 5w)) = 0
(45 + 9w + (25w + 5w2)) = 0

Combine like terms: 9w + 25w = 34w
(45 + 34w + 5w2) = 0

Solving
45 + 34w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + w)(9 + 5w) = 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 '(9 + 5w)' equal to zero and attempt to solve:

Simplifying
9 + 5w = 0

Solving
9 + 5w = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5w = 0 + -9
5w = 0 + -9

Combine like terms: 0 + -9 = -9
5w = -9

Divide each side by '5'.
w = -1.8

Simplifying
w = -1.8
Solution
w = {-5, -1.8}