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

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

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

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

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

Combine like terms: 25w + -9w = 16w
(-45 + 16w + 5w2) = 0

Solving
-45 + 16w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -1w)(9 + -5w) = 0

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

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 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 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
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}