3y(5y^3+2)(5y^3-2)=0

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Solution for 3y(5y^3+2)(5y^3-2)=0 equation: 


Simplifying
3y(5y3 + 2)(5y3 + -2) = 0

Reorder the terms:
3y(2 + 5y3)(5y3 + -2) = 0

Reorder the terms:
3y(2 + 5y3)(-2 + 5y3) = 0

Multiply (2 + 5y3) * (-2 + 5y3)
3y(2(-2 + 5y3) + 5y3 * (-2 + 5y3)) = 0
3y((-2 * 2 + 5y3 * 2) + 5y3 * (-2 + 5y3)) = 0
3y((-4 + 10y3) + 5y3 * (-2 + 5y3)) = 0
3y(-4 + 10y3 + (-2 * 5y3 + 5y3 * 5y3)) = 0
3y(-4 + 10y3 + (-10y3 + 25y6)) = 0

Combine like terms: 10y3 + -10y3 = 0
3y(-4 + 0 + 25y6) = 0
3y(-4 + 25y6) = 0
(-4 * 3y + 25y6 * 3y) = 0
(-12y + 75y7) = 0

Solving
-12y + 75y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-4 + 25y6) = 0

Factor a difference between two squares.
3y((2 + 5y3)(-2 + 5y3)) = 0

Ignore the factor 3.

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 + 5y3)' equal to zero and attempt to solve:

Simplifying
2 + 5y3 = 0

Solving
2 + 5y3 = 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 + 5y3 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5y3 = 0 + -2
5y3 = 0 + -2

Combine like terms: 0 + -2 = -2
5y3 = -2

Divide each side by '5'.
y3 = -0.4

Simplifying
y3 = -0.4

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(-2 + 5y3)' equal to zero and attempt to solve:

Simplifying
-2 + 5y3 = 0

Solving
-2 + 5y3 = 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 + 5y3 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5y3 = 0 + 2
5y3 = 0 + 2

Combine like terms: 0 + 2 = 2
5y3 = 2

Divide each side by '5'.
y3 = 0.4

Simplifying
y3 = 0.4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}

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