3y=4y^3

Solution for 3y=4y^3 equation:

Simplifying
3y = 4y3

Solving
3y = 4y3

Solving for variable 'y'.

Combine like terms: 4y3 + -4y3 = 0
3y + -4y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + -4y2) = 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 '(3 + -4y2)' equal to zero and attempt to solve:

Simplifying
3 + -4y2 = 0

Solving
3 + -4y2 = 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 + -4y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4y2 = 0 + -3
-4y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4y2 = -3

Divide each side by '-4'.
y2 = 0.75

Simplifying
y2 = 0.75

Take the square root of each side:
y = {-0.866025404, 0.866025404}
Solution
y = {0, -0.866025404, 0.866025404}