y+1=(7y-25)(7y-25)

Solution for y+1=(7y-25)(7y-25) equation:

Simplifying
y + 1 = (7y + -25)(7y + -25)

Reorder the terms:
1 + y = (7y + -25)(7y + -25)

Reorder the terms:
1 + y = (-25 + 7y)(7y + -25)

Reorder the terms:
1 + y = (-25 + 7y)(-25 + 7y)

Multiply (-25 + 7y) * (-25 + 7y)
1 + y = (-25(-25 + 7y) + 7y * (-25 + 7y))
1 + y = ((-25 * -25 + 7y * -25) + 7y * (-25 + 7y))
1 + y = ((625 + -175y) + 7y * (-25 + 7y))
1 + y = (625 + -175y + (-25 * 7y + 7y * 7y))
1 + y = (625 + -175y + (-175y + 49y2))

Combine like terms: -175y + -175y = -350y
1 + y = (625 + -350y + 49y2)

Solving
1 + y = 625 + -350y + 49y2

Solving for variable 'y'.

Reorder the terms:
1 + -625 + y + 350y + -49y2 = 625 + -350y + 49y2 + -625 + 350y + -49y2

Combine like terms: 1 + -625 = -624
-624 + y + 350y + -49y2 = 625 + -350y + 49y2 + -625 + 350y + -49y2

Combine like terms: y + 350y = 351y
-624 + 351y + -49y2 = 625 + -350y + 49y2 + -625 + 350y + -49y2

Reorder the terms:
-624 + 351y + -49y2 = 625 + -625 + -350y + 350y + 49y2 + -49y2

Combine like terms: 625 + -625 = 0
-624 + 351y + -49y2 = 0 + -350y + 350y + 49y2 + -49y2
-624 + 351y + -49y2 = -350y + 350y + 49y2 + -49y2

Combine like terms: -350y + 350y = 0
-624 + 351y + -49y2 = 0 + 49y2 + -49y2
-624 + 351y + -49y2 = 49y2 + -49y2

Combine like terms: 49y2 + -49y2 = 0
-624 + 351y + -49y2 = 0

Begin completing the square.  Divide all terms by
-49 the coefficient of the squared term: 

Divide each side by '-49'.
12.73469388 + -7.163265306y + y2 = 0

Move the constant term to the right:

Add '-12.73469388' to each side of the equation.
12.73469388 + -7.163265306y + -12.73469388 + y2 = 0 + -12.73469388

Reorder the terms:
12.73469388 + -12.73469388 + -7.163265306y + y2 = 0 + -12.73469388

Combine like terms: 12.73469388 + -12.73469388 = 0.00000000
0.00000000 + -7.163265306y + y2 = 0 + -12.73469388
-7.163265306y + y2 = 0 + -12.73469388

Combine like terms: 0 + -12.73469388 = -12.73469388
-7.163265306y + y2 = -12.73469388

The y term is -7.163265306y.  Take half its coefficient (-3.581632653).
Square it (12.82809246) and add it to both sides.

Add '12.82809246' to each side of the equation.
-7.163265306y + 12.82809246 + y2 = -12.73469388 + 12.82809246

Reorder the terms:
12.82809246 + -7.163265306y + y2 = -12.73469388 + 12.82809246

Combine like terms: -12.73469388 + 12.82809246 = 0.09339858
12.82809246 + -7.163265306y + y2 = 0.09339858

Factor a perfect square on the left side:
(y + -3.581632653)(y + -3.581632653) = 0.09339858

Calculate the square root of the right side: 0.305611813

Break this problem into two subproblems by setting 
(y + -3.581632653) equal to 0.305611813 and -0.305611813.

Subproblem 1
y + -3.581632653 = 0.305611813

Simplifying
y + -3.581632653 = 0.305611813

Reorder the terms:
-3.581632653 + y = 0.305611813

Solving
-3.581632653 + y = 0.305611813

Solving for variable 'y'.

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

Add '3.581632653' to each side of the equation.
-3.581632653 + 3.581632653 + y = 0.305611813 + 3.581632653

Combine like terms: -3.581632653 + 3.581632653 = 0.000000000
0.000000000 + y = 0.305611813 + 3.581632653
y = 0.305611813 + 3.581632653

Combine like terms: 0.305611813 + 3.581632653 = 3.887244466
y = 3.887244466

Simplifying
y = 3.887244466

Subproblem 2
y + -3.581632653 = -0.305611813

Simplifying
y + -3.581632653 = -0.305611813

Reorder the terms:
-3.581632653 + y = -0.305611813

Solving
-3.581632653 + y = -0.305611813

Solving for variable 'y'.

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

Add '3.581632653' to each side of the equation.
-3.581632653 + 3.581632653 + y = -0.305611813 + 3.581632653

Combine like terms: -3.581632653 + 3.581632653 = 0.000000000
0.000000000 + y = -0.305611813 + 3.581632653
y = -0.305611813 + 3.581632653

Combine like terms: -0.305611813 + 3.581632653 = 3.27602084
y = 3.27602084

Simplifying
y = 3.27602084

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.887244466, 3.27602084}