y^2-4y+9=y+5

Solution for y^2-4y+9=y+5 equation:

Simplifying
y2 + -4y + 9 = y + 5

Reorder the terms:
9 + -4y + y2 = y + 5

Reorder the terms:
9 + -4y + y2 = 5 + y

Solving
9 + -4y + y2 = 5 + y

Solving for variable 'y'.

Reorder the terms:
9 + -5 + -4y + -1y + y2 = 5 + y + -5 + -1y

Combine like terms: 9 + -5 = 4
4 + -4y + -1y + y2 = 5 + y + -5 + -1y

Combine like terms: -4y + -1y = -5y
4 + -5y + y2 = 5 + y + -5 + -1y

Reorder the terms:
4 + -5y + y2 = 5 + -5 + y + -1y

Combine like terms: 5 + -5 = 0
4 + -5y + y2 = 0 + y + -1y
4 + -5y + y2 = y + -1y

Combine like terms: y + -1y = 0
4 + -5y + y2 = 0

Factor a trinomial.
(1 + -1y)(4 + -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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {1, 4}