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

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


Simplifying
5(w + 9)(-1w + 4) = 0

Reorder the terms:
5(9 + w)(-1w + 4) = 0

Reorder the terms:
5(9 + w)(4 + -1w) = 0

Multiply (9 + w) * (4 + -1w)
5(9(4 + -1w) + w(4 + -1w)) = 0
5((4 * 9 + -1w * 9) + w(4 + -1w)) = 0
5((36 + -9w) + w(4 + -1w)) = 0
5(36 + -9w + (4 * w + -1w * w)) = 0
5(36 + -9w + (4w + -1w2)) = 0

Combine like terms: -9w + 4w = -5w
5(36 + -5w + -1w2) = 0
(36 * 5 + -5w * 5 + -1w2 * 5) = 0
(180 + -25w + -5w2) = 0

Solving
180 + -25w + -5w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + -5w + -1w2) = 0

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

Ignore the factor 5.

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 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

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

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

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

Simplifying
w = -9
Solution
w = {4, -9}

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