w^3-2w^2-3w+7=5w+7

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Solution for w^3-2w^2-3w+7=5w+7 equation: 


Simplifying
w3 + -2w2 + -3w + 7 = 5w + 7

Reorder the terms:
7 + -3w + -2w2 + w3 = 5w + 7

Reorder the terms:
7 + -3w + -2w2 + w3 = 7 + 5w

Add '-7' to each side of the equation.
7 + -3w + -2w2 + -7 + w3 = 7 + -7 + 5w

Reorder the terms:
7 + -7 + -3w + -2w2 + w3 = 7 + -7 + 5w

Combine like terms: 7 + -7 = 0
0 + -3w + -2w2 + w3 = 7 + -7 + 5w
-3w + -2w2 + w3 = 7 + -7 + 5w

Combine like terms: 7 + -7 = 0
-3w + -2w2 + w3 = 0 + 5w
-3w + -2w2 + w3 = 5w

Solving
-3w + -2w2 + w3 = 5w

Solving for variable 'w'.

Reorder the terms:
-3w + -5w + -2w2 + w3 = 5w + -5w

Combine like terms: -3w + -5w = -8w
-8w + -2w2 + w3 = 5w + -5w

Combine like terms: 5w + -5w = 0
-8w + -2w2 + w3 = 0

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

Factor a trinomial.
w((-2 + -1w)(4 + -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 '(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
Solution
w = {0, -2, 4}

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