3y^3-7y^2=3y^2+8y

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


Simplifying
3y3 + -7y2 = 3y2 + 8y

Reorder the terms:
-7y2 + 3y3 = 3y2 + 8y

Reorder the terms:
-7y2 + 3y3 = 8y + 3y2

Solving
-7y2 + 3y3 = 8y + 3y2

Solving for variable 'y'.

Reorder the terms:
-8y + -7y2 + -3y2 + 3y3 = 8y + 3y2 + -8y + -3y2

Combine like terms: -7y2 + -3y2 = -10y2
-8y + -10y2 + 3y3 = 8y + 3y2 + -8y + -3y2

Reorder the terms:
-8y + -10y2 + 3y3 = 8y + -8y + 3y2 + -3y2

Combine like terms: 8y + -8y = 0
-8y + -10y2 + 3y3 = 0 + 3y2 + -3y2
-8y + -10y2 + 3y3 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-8y + -10y2 + 3y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8 + -10y + 3y2) = 0

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


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Simplifying
-2 + -3y = 0

Solving
-2 + -3y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3y = 0 + 2
-3y = 0 + 2

Combine like terms: 0 + 2 = 2
-3y = 2

Divide each side by '-3'.
y = -0.6666666667

Simplifying
y = -0.6666666667

Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {0, -0.6666666667, 4}

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