y^2-4y+16=4y+1

Solution for y^2-4y+16=4y+1 equation:

Simplifying
y2 + -4y + 16 = 4y + 1

Reorder the terms:
16 + -4y + y2 = 4y + 1

Reorder the terms:
16 + -4y + y2 = 1 + 4y

Solving
16 + -4y + y2 = 1 + 4y

Solving for variable 'y'.

Reorder the terms:
16 + -1 + -4y + -4y + y2 = 1 + 4y + -1 + -4y

Combine like terms: 16 + -1 = 15
15 + -4y + -4y + y2 = 1 + 4y + -1 + -4y

Combine like terms: -4y + -4y = -8y
15 + -8y + y2 = 1 + 4y + -1 + -4y

Reorder the terms:
15 + -8y + y2 = 1 + -1 + 4y + -4y

Combine like terms: 1 + -1 = 0
15 + -8y + y2 = 0 + 4y + -4y
15 + -8y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
15 + -8y + y2 = 0

Factor a trinomial.
(3 + -1y)(5 + -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 '(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 = {3, 5}