y(y-3)+6=2y

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

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

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

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

Solving
6 + -3y + y2 = 2y

Solving for variable 'y'.

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

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

Combine like terms: 2y + -2y = 0
6 + -5y + y2 = 0

Factor a trinomial.
(2 + -1y)(3 + -1y) = 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 + -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
Solution
y = {2, 3}