4y(y+30)=y+1

Solution for 4y(y+30)=y+1 equation:

Simplifying
4y(y + 30) = y + 1

Reorder the terms:
4y(30 + y) = y + 1
(30 * 4y + y * 4y) = y + 1
(120y + 4y2) = y + 1

Reorder the terms:
120y + 4y2 = 1 + y

Solving
120y + 4y2 = 1 + y

Solving for variable 'y'.

Reorder the terms:
-1 + 120y + -1y + 4y2 = 1 + y + -1 + -1y

Combine like terms: 120y + -1y = 119y
-1 + 119y + 4y2 = 1 + y + -1 + -1y

Reorder the terms:
-1 + 119y + 4y2 = 1 + -1 + y + -1y

Combine like terms: 1 + -1 = 0
-1 + 119y + 4y2 = 0 + y + -1y
-1 + 119y + 4y2 = y + -1y

Combine like terms: y + -1y = 0
-1 + 119y + 4y2 = 0

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

Divide each side by '4'.
-0.25 + 29.75y + y2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 29.75y + 0.25 + y2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 29.75y + y2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 29.75y + y2 = 0 + 0.25
29.75y + y2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
29.75y + y2 = 0.25

The y term is 29.75y.  Take half its coefficient (14.875).
Square it (221.265625) and add it to both sides.

Add '221.265625' to each side of the equation.
29.75y + 221.265625 + y2 = 0.25 + 221.265625

Reorder the terms:
221.265625 + 29.75y + y2 = 0.25 + 221.265625

Combine like terms: 0.25 + 221.265625 = 221.515625
221.265625 + 29.75y + y2 = 221.515625

Factor a perfect square on the left side:
(y + 14.875)(y + 14.875) = 221.515625

Calculate the square root of the right side: 14.883400989

Break this problem into two subproblems by setting 
(y + 14.875) equal to 14.883400989 and -14.883400989.

Subproblem 1
y + 14.875 = 14.883400989

Simplifying
y + 14.875 = 14.883400989

Reorder the terms:
14.875 + y = 14.883400989

Solving
14.875 + y = 14.883400989

Solving for variable 'y'.

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

Add '-14.875' to each side of the equation.
14.875 + -14.875 + y = 14.883400989 + -14.875

Combine like terms: 14.875 + -14.875 = 0.000
0.000 + y = 14.883400989 + -14.875
y = 14.883400989 + -14.875

Combine like terms: 14.883400989 + -14.875 = 0.008400989
y = 0.008400989

Simplifying
y = 0.008400989

Subproblem 2
y + 14.875 = -14.883400989

Simplifying
y + 14.875 = -14.883400989

Reorder the terms:
14.875 + y = -14.883400989

Solving
14.875 + y = -14.883400989

Solving for variable 'y'.

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

Add '-14.875' to each side of the equation.
14.875 + -14.875 + y = -14.883400989 + -14.875

Combine like terms: 14.875 + -14.875 = 0.000
0.000 + y = -14.883400989 + -14.875
y = -14.883400989 + -14.875

Combine like terms: -14.883400989 + -14.875 = -29.758400989
y = -29.758400989

Simplifying
y = -29.758400989

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.008400989, -29.758400989}