y^2-13y+16=-5y+4

Solution for y^2-13y+16=-5y+4 equation:

Simplifying
y2 + -13y + 16 = -5y + 4

Reorder the terms:
16 + -13y + y2 = -5y + 4

Reorder the terms:
16 + -13y + y2 = 4 + -5y

Solving
16 + -13y + y2 = 4 + -5y

Solving for variable 'y'.

Reorder the terms:
16 + -4 + -13y + 5y + y2 = 4 + -5y + -4 + 5y

Combine like terms: 16 + -4 = 12
12 + -13y + 5y + y2 = 4 + -5y + -4 + 5y

Combine like terms: -13y + 5y = -8y
12 + -8y + y2 = 4 + -5y + -4 + 5y

Reorder the terms:
12 + -8y + y2 = 4 + -4 + -5y + 5y

Combine like terms: 4 + -4 = 0
12 + -8y + y2 = 0 + -5y + 5y
12 + -8y + y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
12 + -8y + y2 = 0

Factor a trinomial.
(2 + -1y)(6 + -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 '(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 = {2, 6}