y^2-9y+6=-3y+1

Solution for y^2-9y+6=-3y+1 equation:

Simplifying
y2 + -9y + 6 = -3y + 1

Reorder the terms:
6 + -9y + y2 = -3y + 1

Reorder the terms:
6 + -9y + y2 = 1 + -3y

Solving
6 + -9y + y2 = 1 + -3y

Solving for variable 'y'.

Reorder the terms:
6 + -1 + -9y + 3y + y2 = 1 + -3y + -1 + 3y

Combine like terms: 6 + -1 = 5
5 + -9y + 3y + y2 = 1 + -3y + -1 + 3y

Combine like terms: -9y + 3y = -6y
5 + -6y + y2 = 1 + -3y + -1 + 3y

Reorder the terms:
5 + -6y + y2 = 1 + -1 + -3y + 3y

Combine like terms: 1 + -1 = 0
5 + -6y + y2 = 0 + -3y + 3y
5 + -6y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
5 + -6y + y2 = 0

Factor a trinomial.
(1 + -1y)(5 + -1y) = 0

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

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
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 = {1, 5}