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

Solution for (4+w)(5w-9)=0 equation:

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

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

Multiply (4 + w) * (-9 + 5w)
(4(-9 + 5w) + w(-9 + 5w)) = 0
((-9 * 4 + 5w * 4) + w(-9 + 5w)) = 0
((-36 + 20w) + w(-9 + 5w)) = 0
(-36 + 20w + (-9 * w + 5w * w)) = 0
(-36 + 20w + (-9w + 5w2)) = 0

Combine like terms: 20w + -9w = 11w
(-36 + 11w + 5w2) = 0

Solving
-36 + 11w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -1w)(9 + -5w) = 0

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

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 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 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
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 = {-4, 1.8}