5y^3=3y-4y^3

Solution for 5y^3=3y-4y^3 equation:

Simplifying
5y3 = 3y + -4y3

Solving
5y3 = 3y + -4y3

Solving for variable 'y'.

Reorder the terms:
-3y + 5y3 + 4y3 = 3y + -4y3 + -3y + 4y3

Combine like terms: 5y3 + 4y3 = 9y3
-3y + 9y3 = 3y + -4y3 + -3y + 4y3

Reorder the terms:
-3y + 9y3 = 3y + -3y + -4y3 + 4y3

Combine like terms: 3y + -3y = 0
-3y + 9y3 = 0 + -4y3 + 4y3
-3y + 9y3 = -4y3 + 4y3

Combine like terms: -4y3 + 4y3 = 0
-3y + 9y3 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-1 + 3y2) = 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 '(-1 + 3y2)' equal to zero and attempt to solve:

Simplifying
-1 + 3y2 = 0

Solving
-1 + 3y2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 3y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3y2 = 0 + 1
3y2 = 0 + 1

Combine like terms: 0 + 1 = 1
3y2 = 1

Divide each side by '3'.
y2 = 0.3333333333

Simplifying
y2 = 0.3333333333

Take the square root of each side:
y = {-0.577350269, 0.577350269}
Solution
y = {0, -0.577350269, 0.577350269}