y^2-6y+9=2(y-3)

Solution for y^2-6y+9=2(y-3) equation:

Simplifying
y2 + -6y + 9 = 2(y + -3)

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

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

Solving
9 + -6y + y2 = -6 + 2y

Solving for variable 'y'.

Reorder the terms:
9 + 6 + -6y + -2y + y2 = -6 + 2y + 6 + -2y

Combine like terms: 9 + 6 = 15
15 + -6y + -2y + y2 = -6 + 2y + 6 + -2y

Combine like terms: -6y + -2y = -8y
15 + -8y + y2 = -6 + 2y + 6 + -2y

Reorder the terms:
15 + -8y + y2 = -6 + 6 + 2y + -2y

Combine like terms: -6 + 6 = 0
15 + -8y + y2 = 0 + 2y + -2y
15 + -8y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
15 + -8y + y2 = 0

Factor a trinomial.
(3 + -1y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {3, 5}