w^3-5w^2-6w+9=8w+9

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Solution for w^3-5w^2-6w+9=8w+9 equation: 


Simplifying
w3 + -5w2 + -6w + 9 = 8w + 9

Reorder the terms:
9 + -6w + -5w2 + w3 = 8w + 9

Reorder the terms:
9 + -6w + -5w2 + w3 = 9 + 8w

Add '-9' to each side of the equation.
9 + -6w + -5w2 + -9 + w3 = 9 + -9 + 8w

Reorder the terms:
9 + -9 + -6w + -5w2 + w3 = 9 + -9 + 8w

Combine like terms: 9 + -9 = 0
0 + -6w + -5w2 + w3 = 9 + -9 + 8w
-6w + -5w2 + w3 = 9 + -9 + 8w

Combine like terms: 9 + -9 = 0
-6w + -5w2 + w3 = 0 + 8w
-6w + -5w2 + w3 = 8w

Solving
-6w + -5w2 + w3 = 8w

Solving for variable 'w'.

Reorder the terms:
-6w + -8w + -5w2 + w3 = 8w + -8w

Combine like terms: -6w + -8w = -14w
-14w + -5w2 + w3 = 8w + -8w

Combine like terms: 8w + -8w = 0
-14w + -5w2 + w3 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-14 + -5w + w2) = 0

Factor a trinomial.
w((-2 + -1w)(7 + -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 '(-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

Subproblem 3
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {0, -2, 7}

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