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

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


Simplifying
(3y3 + 2y)(y2 + -2) = 0

Reorder the terms:
(2y + 3y3)(y2 + -2) = 0

Reorder the terms:
(2y + 3y3)(-2 + y2) = 0

Multiply (2y + 3y3) * (-2 + y2)
(2y * (-2 + y2) + 3y3 * (-2 + y2)) = 0
((-2 * 2y + y2 * 2y) + 3y3 * (-2 + y2)) = 0
((-4y + 2y3) + 3y3 * (-2 + y2)) = 0
(-4y + 2y3 + (-2 * 3y3 + y2 * 3y3)) = 0
(-4y + 2y3 + (-6y3 + 3y5)) = 0

Combine like terms: 2y3 + -6y3 = -4y3
(-4y + -4y3 + 3y5) = 0

Solving
-4y + -4y3 + 3y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + -4y2 + 3y4) = 0

Factor a trinomial.
y((-2 + -3y2)(2 + -1y2)) = 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 + -3y2)' equal to zero and attempt to solve:

Simplifying
-2 + -3y2 = 0

Solving
-2 + -3y2 = 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 + -3y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3y2 = 0 + 2
-3y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3y2 = 2

Divide each side by '-3'.
y2 = -0.6666666667

Simplifying
y2 = -0.6666666667

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 + -1y2)' equal to zero and attempt to solve:

Simplifying
2 + -1y2 = 0

Solving
2 + -1y2 = 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 + -1y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y2 = 0 + -2
-1y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1y2 = -2

Divide each side by '-1'.
y2 = 2

Simplifying
y2 = 2

Take the square root of each side:
y = {-1.414213562, 1.414213562}
Solution
y = {0, -1.414213562, 1.414213562}

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