y(3y-2)-6=3y(1-y)

Solution for y(3y-2)-6=3y(1-y) equation:

Simplifying
y(3y + -2) + -6 = 3y(1 + -1y)

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

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

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

Solving for variable 'y'.

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

Combine like terms: -2y + -3y = -5y
-6 + -5y + 3y2 + 3y2 = 3y + -3y2 + -3y + 3y2

Combine like terms: 3y2 + 3y2 = 6y2
-6 + -5y + 6y2 = 3y + -3y2 + -3y + 3y2

Reorder the terms:
-6 + -5y + 6y2 = 3y + -3y + -3y2 + 3y2

Combine like terms: 3y + -3y = 0
-6 + -5y + 6y2 = 0 + -3y2 + 3y2
-6 + -5y + 6y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-6 + -5y + 6y2 = 0

Factor a trinomial.
(-2 + -3y)(3 + -2y) = 0

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

Simplifying
-2 + -3y = 0

Solving
-2 + -3y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3y = 0 + 2
-3y = 0 + 2

Combine like terms: 0 + 2 = 2
-3y = 2

Divide each side by '-3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-0.6666666667, 1.5}