(y*y)-6y+15=3y-3

Solution for (y*y)-6y+15=3y-3 equation:

Simplifying
(y * y) + -6y + 15 = 3y + -3

Multiply y * y
(y2) + -6y + 15 = 3y + -3
y2 + -6y + 15 = 3y + -3

Reorder the terms:
15 + -6y + y2 = 3y + -3

Reorder the terms:
15 + -6y + y2 = -3 + 3y

Solving
15 + -6y + y2 = -3 + 3y

Solving for variable 'y'.

Reorder the terms:
15 + 3 + -6y + -3y + y2 = -3 + 3y + 3 + -3y

Combine like terms: 15 + 3 = 18
18 + -6y + -3y + y2 = -3 + 3y + 3 + -3y

Combine like terms: -6y + -3y = -9y
18 + -9y + y2 = -3 + 3y + 3 + -3y

Reorder the terms:
18 + -9y + y2 = -3 + 3 + 3y + -3y

Combine like terms: -3 + 3 = 0
18 + -9y + y2 = 0 + 3y + -3y
18 + -9y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
18 + -9y + y2 = 0

Factor a trinomial.
(3 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

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

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

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {3, 6}