4y^2-4y+1=25

Solution for 4y^2-4y+1=25 equation:

Simplifying
4y2 + -4y + 1 = 25

Reorder the terms:
1 + -4y + 4y2 = 25

Solving
1 + -4y + 4y2 = 25

Solving for variable 'y'.

Reorder the terms:
1 + -25 + -4y + 4y2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + -4y + 4y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + -4y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -1y + y2) = 0

Factor a trinomial.
4((-2 + -1y)(3 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -1y)' equal to zero and attempt to solve:

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
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
Solution
y = {-2, 3}