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

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

Simplifying
(6y3 + 4y2) + -1(2y2 + 3y) = 0

Reorder the terms:
(4y2 + 6y3) + -1(2y2 + 3y) = 0

Remove parenthesis around (4y2 + 6y3)
4y2 + 6y3 + -1(2y2 + 3y) = 0

Reorder the terms:
4y2 + 6y3 + -1(3y + 2y2) = 0
4y2 + 6y3 + (3y * -1 + 2y2 * -1) = 0
4y2 + 6y3 + (-3y + -2y2) = 0

Reorder the terms:
-3y + 4y2 + -2y2 + 6y3 = 0

Combine like terms: 4y2 + -2y2 = 2y2
-3y + 2y2 + 6y3 = 0

Solving
-3y + 2y2 + 6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-3 + 2y + 6y2) = 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 + 2y + 6y2)' equal to zero and attempt to solve:

Simplifying
-3 + 2y + 6y2 = 0

Solving
-3 + 2y + 6y2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.5 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.3333333333y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.3333333333y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.3333333333y + y2 = 0 + 0.5
0.3333333333y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.3333333333y + y2 = 0.5

The y term is 0.3333333333y.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333y + 0.02777777779 + y2 = 0.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333y + y2 = 0.5 + 0.02777777779

Combine like terms: 0.5 + 0.02777777779 = 0.52777777779
0.02777777779 + 0.3333333333y + y2 = 0.52777777779

Factor a perfect square on the left side:
(y + 0.1666666667)(y + 0.1666666667) = 0.52777777779

Calculate the square root of the right side: 0.726483157

Break this problem into two subproblems by setting 
(y + 0.1666666667) equal to 0.726483157 and -0.726483157.

Subproblem 1
y + 0.1666666667 = 0.726483157

Simplifying
y + 0.1666666667 = 0.726483157

Reorder the terms:
0.1666666667 + y = 0.726483157

Solving
0.1666666667 + y = 0.726483157

Solving for variable 'y'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + y = 0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + y = 0.726483157 + -0.1666666667
y = 0.726483157 + -0.1666666667

Combine like terms: 0.726483157 + -0.1666666667 = 0.5598164903
y = 0.5598164903

Simplifying
y = 0.5598164903

Subproblem 2
y + 0.1666666667 = -0.726483157

Simplifying
y + 0.1666666667 = -0.726483157

Reorder the terms:
0.1666666667 + y = -0.726483157

Solving
0.1666666667 + y = -0.726483157

Solving for variable 'y'.

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

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + y = -0.726483157 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + y = -0.726483157 + -0.1666666667
y = -0.726483157 + -0.1666666667

Combine like terms: -0.726483157 + -0.1666666667 = -0.8931498237
y = -0.8931498237

Simplifying
y = -0.8931498237

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.5598164903, -0.8931498237}
Solution
y = {0, 0.5598164903, -0.8931498237}