1+6y(4y-25)=5

Solution for 1+6y(4y-25)=5 equation:

Simplifying
1 + 6y(4y + -25) = 5

Reorder the terms:
1 + 6y(-25 + 4y) = 5
1 + (-25 * 6y + 4y * 6y) = 5
1 + (-150y + 24y2) = 5

Solving
1 + -150y + 24y2 = 5

Solving for variable 'y'.

Reorder the terms:
1 + -5 + -150y + 24y2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + -150y + 24y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + -150y + 24y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -75y + 12y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -75y + 12y2)' equal to zero and attempt to solve:

Simplifying
-2 + -75y + 12y2 = 0

Solving
-2 + -75y + 12y2 = 0

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

Divide each side by '12'.
-0.1666666667 + -6.25y + y2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -6.25y + 0.1666666667 + y2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -6.25y + y2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -6.25y + y2 = 0 + 0.1666666667
-6.25y + y2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-6.25y + y2 = 0.1666666667

The y term is -6.25y.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25y + 9.765625 + y2 = 0.1666666667 + 9.765625

Reorder the terms:
9.765625 + -6.25y + y2 = 0.1666666667 + 9.765625

Combine like terms: 0.1666666667 + 9.765625 = 9.9322916667
9.765625 + -6.25y + y2 = 9.9322916667

Factor a perfect square on the left side:
(y + -3.125)(y + -3.125) = 9.9322916667

Calculate the square root of the right side: 3.15155385

Break this problem into two subproblems by setting 
(y + -3.125) equal to 3.15155385 and -3.15155385.

Subproblem 1
y + -3.125 = 3.15155385

Simplifying
y + -3.125 = 3.15155385

Reorder the terms:
-3.125 + y = 3.15155385

Solving
-3.125 + y = 3.15155385

Solving for variable 'y'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + y = 3.15155385 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + y = 3.15155385 + 3.125
y = 3.15155385 + 3.125

Combine like terms: 3.15155385 + 3.125 = 6.27655385
y = 6.27655385

Simplifying
y = 6.27655385

Subproblem 2
y + -3.125 = -3.15155385

Simplifying
y + -3.125 = -3.15155385

Reorder the terms:
-3.125 + y = -3.15155385

Solving
-3.125 + y = -3.15155385

Solving for variable 'y'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + y = -3.15155385 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + y = -3.15155385 + 3.125
y = -3.15155385 + 3.125

Combine like terms: -3.15155385 + 3.125 = -0.02655385
y = -0.02655385

Simplifying
y = -0.02655385

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.27655385, -0.02655385}
Solution
y = {6.27655385, -0.02655385}