2y^2(-6y+3)+4y^3=0

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Solution for 2y^2(-6y+3)+4y^3=0 equation: 


Simplifying
2y2(-6y + 3) + 4y3 = 0

Reorder the terms:
2y2(3 + -6y) + 4y3 = 0
(3 * 2y2 + -6y * 2y2) + 4y3 = 0
(6y2 + -12y3) + 4y3 = 0

Combine like terms: -12y3 + 4y3 = -8y3
6y2 + -8y3 = 0

Solving
6y2 + -8y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(3 + -4y) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

Subproblem 2
Set the factor '(3 + -4y)' equal to zero and attempt to solve:

Simplifying
3 + -4y = 0

Solving
3 + -4y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y = 0 + -3
-4y = 0 + -3

Combine like terms: 0 + -3 = -3
-4y = -3

Divide each side by '-4'.
y = 0.75

Simplifying
y = 0.75
Solution
y = {0, 0.75}

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