6y^3+5y^2=4y

Solution for 6y^3+5y^2=4y equation:

Simplifying
6y3 + 5y2 = 4y

Reorder the terms:
5y2 + 6y3 = 4y

Solving
5y2 + 6y3 = 4y

Solving for variable 'y'.

Reorder the terms:
-4y + 5y2 + 6y3 = 4y + -4y

Combine like terms: 4y + -4y = 0
-4y + 5y2 + 6y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + 5y + 6y2) = 0

Factor a trinomial.
y((-4 + -3y)(1 + -2y)) = 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 '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 0

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

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

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

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

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333
Subproblem 3
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {0, -1.333333333, 0.5}