3y^3-10y^2=3y^2+10y

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Solution for 3y^3-10y^2=3y^2+10y equation: 


Simplifying
3y3 + -10y2 = 3y2 + 10y

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

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

Solving
-10y2 + 3y3 = 10y + 3y2

Solving for variable 'y'.

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

Combine like terms: -10y2 + -3y2 = -13y2
-10y + -13y2 + 3y3 = 10y + 3y2 + -10y + -3y2

Reorder the terms:
-10y + -13y2 + 3y3 = 10y + -10y + 3y2 + -3y2

Combine like terms: 10y + -10y = 0
-10y + -13y2 + 3y3 = 0 + 3y2 + -3y2
-10y + -13y2 + 3y3 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-10y + -13y2 + 3y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-10 + -13y + 3y2) = 0

Factor a trinomial.
y((-2 + -3y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {0, -0.6666666667, 5}

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