y^3-25y=3(y-5)y

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Solution for y^3-25y=3(y-5)y equation: 


Simplifying
y3 + -25y = 3(y + -5) * y

Reorder the terms:
-25y + y3 = 3(y + -5) * y

Reorder the terms:
-25y + y3 = 3(-5 + y) * y

Reorder the terms for easier multiplication:
-25y + y3 = 3y(-5 + y)
-25y + y3 = (-5 * 3y + y * 3y)
-25y + y3 = (-15y + 3y2)

Solving
-25y + y3 = -15y + 3y2

Solving for variable 'y'.

Reorder the terms:
-25y + 15y + -3y2 + y3 = -15y + 3y2 + 15y + -3y2

Combine like terms: -25y + 15y = -10y
-10y + -3y2 + y3 = -15y + 3y2 + 15y + -3y2

Reorder the terms:
-10y + -3y2 + y3 = -15y + 15y + 3y2 + -3y2

Combine like terms: -15y + 15y = 0
-10y + -3y2 + y3 = 0 + 3y2 + -3y2
-10y + -3y2 + y3 = 3y2 + -3y2

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

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

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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, -2, 5}

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