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

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

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

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

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

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

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

Reorder the terms:
6 + -5y + y2 = 6(-3 + y)
6 + -5y + y2 = (-3 * 6 + y * 6)
6 + -5y + y2 = (-18 + 6y)

Solving
6 + -5y + y2 = -18 + 6y

Solving for variable 'y'.

Reorder the terms:
6 + 18 + -5y + -6y + y2 = -18 + 6y + 18 + -6y

Combine like terms: 6 + 18 = 24
24 + -5y + -6y + y2 = -18 + 6y + 18 + -6y

Combine like terms: -5y + -6y = -11y
24 + -11y + y2 = -18 + 6y + 18 + -6y

Reorder the terms:
24 + -11y + y2 = -18 + 18 + 6y + -6y

Combine like terms: -18 + 18 = 0
24 + -11y + y2 = 0 + 6y + -6y
24 + -11y + y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
24 + -11y + y2 = 0

Factor a trinomial.
(3 + -1y)(8 + -1y) = 0

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

Simplifying
3 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {3, 8}