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

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


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

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

Multiply (9 + w) * (-4 + 5w)
(9(-4 + 5w) + w(-4 + 5w)) = 0
((-4 * 9 + 5w * 9) + w(-4 + 5w)) = 0
((-36 + 45w) + w(-4 + 5w)) = 0
(-36 + 45w + (-4 * w + 5w * w)) = 0
(-36 + 45w + (-4w + 5w2)) = 0

Combine like terms: 45w + -4w = 41w
(-36 + 41w + 5w2) = 0

Solving
-36 + 41w + 5w2 = 0

Solving for variable 'w'.

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


Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve:

Simplifying
-9 + -1w = 0

Solving
-9 + -1w = 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 + -1w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w = 0 + 9
-1w = 0 + 9

Combine like terms: 0 + 9 = 9
-1w = 9

Divide each side by '-1'.
w = -9

Simplifying
w = -9

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 = {-9, 0.8}

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