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

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

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

Reorder the terms:
3y(-3 + 2y) = -4y + 6
(-3 * 3y + 2y * 3y) = -4y + 6
(-9y + 6y2) = -4y + 6

Reorder the terms:
-9y + 6y2 = 6 + -4y

Solving
-9y + 6y2 = 6 + -4y

Solving for variable 'y'.

Reorder the terms:
-6 + -9y + 4y + 6y2 = 6 + -4y + -6 + 4y

Combine like terms: -9y + 4y = -5y
-6 + -5y + 6y2 = 6 + -4y + -6 + 4y

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

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

Combine like terms: -4y + 4y = 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}