0=3y^5-48y^3

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Solution for 0=3y^5-48y^3 equation: 


Simplifying
0 = 3y5 + -48y3

Reorder the terms:
0 = -48y3 + 3y5

Solving
0 = -48y3 + 3y5

Solving for variable 'y'.
Remove the zero:
48y3 + -3y5 = -48y3 + 3y5 + 48y3 + -3y5

Reorder the terms:
48y3 + -3y5 = -48y3 + 48y3 + 3y5 + -3y5

Combine like terms: -48y3 + 48y3 = 0
48y3 + -3y5 = 0 + 3y5 + -3y5
48y3 + -3y5 = 3y5 + -3y5

Combine like terms: 3y5 + -3y5 = 0
48y3 + -3y5 = 0

Factor out the Greatest Common Factor (GCF), '3y3'.
3y3(16 + -1y2) = 0

Factor a difference between two squares.
3y3((4 + y)(4 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

Simplifying
y = -4

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 = {-4, 4}

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