y^2-2y+1=25

Solution for y^2-2y+1=25 equation:

Simplifying
y2 + -2y + 1 = 25

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

Solving
1 + -2y + y2 = 25

Solving for variable 'y'.

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

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

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

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}