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

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

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

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

Remove parenthesis around (-3 + 4y)
-3 + 4y = 3y(y + -2)

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

Solving
-3 + 4y = -6y + 3y2

Solving for variable 'y'.

Combine like terms: 4y + 6y = 10y
-3 + 10y + -3y2 = -6y + 3y2 + 6y + -3y2

Reorder the terms:
-3 + 10y + -3y2 = -6y + 6y + 3y2 + -3y2

Combine like terms: -6y + 6y = 0
-3 + 10y + -3y2 = 0 + 3y2 + -3y2
-3 + 10y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-3 + 10y + -3y2 = 0

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

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

Simplifying
-3 + y = 0

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

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

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

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {3, 0.3333333333}