(5+w)(2w+9)=0

Solution for (5+w)(2w+9)=0 equation:

Simplifying
(5 + w)(2w + 9) = 0

Reorder the terms:
(5 + w)(9 + 2w) = 0

Multiply (5 + w) * (9 + 2w)
(5(9 + 2w) + w(9 + 2w)) = 0
((9 * 5 + 2w * 5) + w(9 + 2w)) = 0
((45 + 10w) + w(9 + 2w)) = 0
(45 + 10w + (9 * w + 2w * w)) = 0
(45 + 10w + (9w + 2w2)) = 0

Combine like terms: 10w + 9w = 19w
(45 + 19w + 2w2) = 0

Solving
45 + 19w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + w)(9 + 2w) = 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 + 2w)' equal to zero and attempt to solve:

Simplifying
9 + 2w = 0

Solving
9 + 2w = 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 + 2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2w = 0 + -9
2w = 0 + -9

Combine like terms: 0 + -9 = -9
2w = -9

Divide each side by '2'.
w = -4.5

Simplifying
w = -4.5
Solution
w = {-5, -4.5}