6y(3y^2-2)=0

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Solution for 6y(3y^2-2)=0 equation: 


Simplifying
6y(3y2 + -2) = 0

Reorder the terms:
6y(-2 + 3y2) = 0
(-2 * 6y + 3y2 * 6y) = 0
(-12y + 18y3) = 0

Solving
-12y + 18y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6y'.
6y(-2 + 3y2) = 0

Ignore the factor 6.

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

Take the square root of each side:
y = {-0.816496581, 0.816496581}
Solution
y = {0, -0.816496581, 0.816496581}

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