3w^3=2w^2+8w

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Solution for 3w^3=2w^2+8w equation: 


Simplifying
3w3 = 2w2 + 8w

Reorder the terms:
3w3 = 8w + 2w2

Solving
3w3 = 8w + 2w2

Solving for variable 'w'.

Reorder the terms:
-8w + -2w2 + 3w3 = 8w + 2w2 + -8w + -2w2

Reorder the terms:
-8w + -2w2 + 3w3 = 8w + -8w + 2w2 + -2w2

Combine like terms: 8w + -8w = 0
-8w + -2w2 + 3w3 = 0 + 2w2 + -2w2
-8w + -2w2 + 3w3 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-8w + -2w2 + 3w3 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-8 + -2w + 3w2) = 0

Factor a trinomial.
w((-4 + -3w)(2 + -1w)) = 0


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 + -3w)' equal to zero and attempt to solve:

Simplifying
-4 + -3w = 0

Solving
-4 + -3w = 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 + -3w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3w = 0 + 4
-3w = 0 + 4

Combine like terms: 0 + 4 = 4
-3w = 4

Divide each side by '-3'.
w = -1.333333333

Simplifying
w = -1.333333333

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {0, -1.333333333, 2}

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