(y-1)(y-1)=16

Solution for (y-1)(y-1)=16 equation:

Simplifying
(y + -1)(y + -1) = 16

Reorder the terms:
(-1 + y)(y + -1) = 16

Reorder the terms:
(-1 + y)(-1 + y) = 16

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) = 16
((-1 * -1 + y * -1) + y(-1 + y)) = 16
((1 + -1y) + y(-1 + y)) = 16
(1 + -1y + (-1 * y + y * y)) = 16
(1 + -1y + (-1y + y2)) = 16

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) = 16

Solving
1 + -2y + y2 = 16

Solving for variable 'y'.

Reorder the terms:
1 + -16 + -2y + y2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + -2y + y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + -2y + 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}