w^3-2w^2-17w+8=7w+8

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Solution for w^3-2w^2-17w+8=7w+8 equation: 


Simplifying
w3 + -2w2 + -17w + 8 = 7w + 8

Reorder the terms:
8 + -17w + -2w2 + w3 = 7w + 8

Reorder the terms:
8 + -17w + -2w2 + w3 = 8 + 7w

Add '-8' to each side of the equation.
8 + -17w + -2w2 + -8 + w3 = 8 + -8 + 7w

Reorder the terms:
8 + -8 + -17w + -2w2 + w3 = 8 + -8 + 7w

Combine like terms: 8 + -8 = 0
0 + -17w + -2w2 + w3 = 8 + -8 + 7w
-17w + -2w2 + w3 = 8 + -8 + 7w

Combine like terms: 8 + -8 = 0
-17w + -2w2 + w3 = 0 + 7w
-17w + -2w2 + w3 = 7w

Solving
-17w + -2w2 + w3 = 7w

Solving for variable 'w'.

Reorder the terms:
-17w + -7w + -2w2 + w3 = 7w + -7w

Combine like terms: -17w + -7w = -24w
-24w + -2w2 + w3 = 7w + -7w

Combine like terms: 7w + -7w = 0
-24w + -2w2 + w3 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-24 + -2w + w2) = 0

Factor a trinomial.
w((-4 + -1w)(6 + -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 + -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 '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {0, -4, 6}

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