(y-4)+y^2=16

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

Simplifying
(y + -4) + y2 = 16

Reorder the terms:
(-4 + y) + y2 = 16

Remove parenthesis around (-4 + y)
-4 + y + y2 = 16

Solving
-4 + y + y2 = 16

Solving for variable 'y'.

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

Combine like terms: -4 + -16 = -20
-20 + y + y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-20 + y + y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -1y) = 0

Subproblem 1
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
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 = {-5, 4}