=(w)*(w-4)*((2*w)+10)

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Solution for =(w)*(w-4)*((2*w)+10) equation: 


Simplifying
0 = (w)(w + -4)((2w) + 10)

Reorder the terms:
0 = w(-4 + w)((2w) + 10)

Reorder the terms:
0 = w(-4 + w)(10 + (2w))

Multiply (-4 + w) * (10 + (2w))
0 = w(-4(10 + (2w)) + w(10 + (2w)))
0 = w((10 * -4 + (2w) * -4) + w(10 + (2w)))
0 = w((-40 + -8w) + w(10 + (2w)))
0 = w(-40 + -8w + (10 * w + (2w) * w))
0 = w(-40 + -8w + (10w + 2w2))

Combine like terms: -8w + 10w = 2w
0 = w(-40 + 2w + 2w2)
0 = (-40 * w + 2w * w + 2w2 * w)
0 = (-40w + 2w2 + 2w3)

Solving
0 = -40w + 2w2 + 2w3

Solving for variable 'w'.
Remove the zero:
40w + -2w2 + -2w3 = -40w + 2w2 + 2w3 + 40w + -2w2 + -2w3

Reorder the terms:
40w + -2w2 + -2w3 = -40w + 40w + 2w2 + -2w2 + 2w3 + -2w3

Combine like terms: -40w + 40w = 0
40w + -2w2 + -2w3 = 0 + 2w2 + -2w2 + 2w3 + -2w3
40w + -2w2 + -2w3 = 2w2 + -2w2 + 2w3 + -2w3

Combine like terms: 2w2 + -2w2 = 0
40w + -2w2 + -2w3 = 0 + 2w3 + -2w3
40w + -2w2 + -2w3 = 2w3 + -2w3

Combine like terms: 2w3 + -2w3 = 0
40w + -2w2 + -2w3 = 0

Factor out the Greatest Common Factor (GCF), '2w'.
2w(20 + -1w + -1w2) = 0

Factor a trinomial.
2w((4 + -1w)(5 + w)) = 0

Ignore the factor 2.

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 '(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 3
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

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

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

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

Simplifying
w = -5
Solution
w = {0, 4, -5}

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