3y^3+y=4y^2

Solution for 3y^3+y=4y^2 equation:

Simplifying
3y3 + y = 4y2

Reorder the terms:
y + 3y3 = 4y2

Solving
y + 3y3 = 4y2

Solving for variable 'y'.

Reorder the terms:
y + -4y2 + 3y3 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
y + -4y2 + 3y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + -4y + 3y2) = 0

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

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

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

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Subproblem 3
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Solution
y = {0, 0.3333333333, 1}