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

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

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

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

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

Multiply (-3 + 4y) * (-2 + y)
(-3(-2 + y) + 4y * (-2 + y)) = 6y(y + -2)
((-2 * -3 + y * -3) + 4y * (-2 + y)) = 6y(y + -2)
((6 + -3y) + 4y * (-2 + y)) = 6y(y + -2)
(6 + -3y + (-2 * 4y + y * 4y)) = 6y(y + -2)
(6 + -3y + (-8y + 4y2)) = 6y(y + -2)

Combine like terms: -3y + -8y = -11y
(6 + -11y + 4y2) = 6y(y + -2)

Reorder the terms:
6 + -11y + 4y2 = 6y(-2 + y)
6 + -11y + 4y2 = (-2 * 6y + y * 6y)
6 + -11y + 4y2 = (-12y + 6y2)

Solving
6 + -11y + 4y2 = -12y + 6y2

Solving for variable 'y'.

Reorder the terms:
6 + -11y + 12y + 4y2 + -6y2 = -12y + 6y2 + 12y + -6y2

Combine like terms: -11y + 12y = 1y
6 + 1y + 4y2 + -6y2 = -12y + 6y2 + 12y + -6y2

Combine like terms: 4y2 + -6y2 = -2y2
6 + 1y + -2y2 = -12y + 6y2 + 12y + -6y2

Reorder the terms:
6 + 1y + -2y2 = -12y + 12y + 6y2 + -6y2

Combine like terms: -12y + 12y = 0
6 + 1y + -2y2 = 0 + 6y2 + -6y2
6 + 1y + -2y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
6 + 1y + -2y2 = 0

Factor a trinomial.
(2 + -1y)(3 + 2y) = 0

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

Simplifying
2 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
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 = {2, -1.5}