(y-1)(y-1)-25=0

Solution for (y-1)(y-1)-25=0 equation:

Simplifying
(y + -1)(y + -1) + -25 = 0

Reorder the terms:
(-1 + y)(y + -1) + -25 = 0

Reorder the terms:
(-1 + y)(-1 + y) + -25 = 0

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) + -25 = 0
((-1 * -1 + y * -1) + y(-1 + y)) + -25 = 0
((1 + -1y) + y(-1 + y)) + -25 = 0
(1 + -1y + (-1 * y + y * y)) + -25 = 0
(1 + -1y + (-1y + y2)) + -25 = 0

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) + -25 = 0

Reorder the terms:
1 + -25 + -2y + y2 = 0

Combine like terms: 1 + -25 = -24
-24 + -2y + y2 = 0

Solving
-24 + -2y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(6 + -1y) = 0

Subproblem 1
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
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 = {-4, 6}