w^3-2w^2-7w+9=8w+9

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Solution for w^3-2w^2-7w+9=8w+9 equation: 


Simplifying
w3 + -2w2 + -7w + 9 = 8w + 9

Reorder the terms:
9 + -7w + -2w2 + w3 = 8w + 9

Reorder the terms:
9 + -7w + -2w2 + w3 = 9 + 8w

Add '-9' to each side of the equation.
9 + -7w + -2w2 + -9 + w3 = 9 + -9 + 8w

Reorder the terms:
9 + -9 + -7w + -2w2 + w3 = 9 + -9 + 8w

Combine like terms: 9 + -9 = 0
0 + -7w + -2w2 + w3 = 9 + -9 + 8w
-7w + -2w2 + w3 = 9 + -9 + 8w

Combine like terms: 9 + -9 = 0
-7w + -2w2 + w3 = 0 + 8w
-7w + -2w2 + w3 = 8w

Solving
-7w + -2w2 + w3 = 8w

Solving for variable 'w'.

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

Combine like terms: -7w + -8w = -15w
-15w + -2w2 + w3 = 8w + -8w

Combine like terms: 8w + -8w = 0
-15w + -2w2 + w3 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-15 + -2w + w2) = 0

Factor a trinomial.
w((-3 + -1w)(5 + -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 '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3

Subproblem 3
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
Solution
w = {0, -3, 5}

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