w(3w+15)(w-8)=0

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Solution for w(3w+15)(w-8)=0 equation: 


Simplifying
w(3w + 15)(w + -8) = 0

Reorder the terms:
w(15 + 3w)(w + -8) = 0

Reorder the terms:
w(15 + 3w)(-8 + w) = 0

Multiply (15 + 3w) * (-8 + w)
w(15(-8 + w) + 3w * (-8 + w)) = 0
w((-8 * 15 + w * 15) + 3w * (-8 + w)) = 0
w((-120 + 15w) + 3w * (-8 + w)) = 0
w(-120 + 15w + (-8 * 3w + w * 3w)) = 0
w(-120 + 15w + (-24w + 3w2)) = 0

Combine like terms: 15w + -24w = -9w
w(-120 + -9w + 3w2) = 0
(-120 * w + -9w * w + 3w2 * w) = 0
(-120w + -9w2 + 3w3) = 0

Solving
-120w + -9w2 + 3w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(-40 + -3w + w2) = 0

Factor a trinomial.
3w((-5 + -1w)(8 + -1w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

Move all terms containing w to the left, all other terms to the right.

Simplifying
w = 0

Subproblem 2
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 3
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {0, -5, 8}

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