(60y+5)(y-2)=60

Solution for (60y+5)(y-2)=60 equation:

Simplifying
(60y + 5)(y + -2) = 60

Reorder the terms:
(5 + 60y)(y + -2) = 60

Reorder the terms:
(5 + 60y)(-2 + y) = 60

Multiply (5 + 60y) * (-2 + y)
(5(-2 + y) + 60y * (-2 + y)) = 60
((-2 * 5 + y * 5) + 60y * (-2 + y)) = 60
((-10 + 5y) + 60y * (-2 + y)) = 60
(-10 + 5y + (-2 * 60y + y * 60y)) = 60
(-10 + 5y + (-120y + 60y2)) = 60

Combine like terms: 5y + -120y = -115y
(-10 + -115y + 60y2) = 60

Solving
-10 + -115y + 60y2 = 60

Solving for variable 'y'.

Reorder the terms:
-10 + -60 + -115y + 60y2 = 60 + -60

Combine like terms: -10 + -60 = -70
-70 + -115y + 60y2 = 60 + -60

Combine like terms: 60 + -60 = 0
-70 + -115y + 60y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-14 + -23y + 12y2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-14 + -23y + 12y2)' equal to zero and attempt to solve:

Simplifying
-14 + -23y + 12y2 = 0

Solving
-14 + -23y + 12y2 = 0

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

Divide each side by '12'.
-1.166666667 + -1.916666667y + y2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -1.916666667y + 1.166666667 + y2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -1.916666667y + y2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -1.916666667y + y2 = 0 + 1.166666667
-1.916666667y + y2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-1.916666667y + y2 = 1.166666667

The y term is -1.916666667y.  Take half its coefficient (-0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
-1.916666667y + 0.9184027781 + y2 = 1.166666667 + 0.9184027781

Reorder the terms:
0.9184027781 + -1.916666667y + y2 = 1.166666667 + 0.9184027781

Combine like terms: 1.166666667 + 0.9184027781 = 2.0850694451
0.9184027781 + -1.916666667y + y2 = 2.0850694451

Factor a perfect square on the left side:
(y + -0.9583333335)(y + -0.9583333335) = 2.0850694451

Calculate the square root of the right side: 1.443976954

Break this problem into two subproblems by setting 
(y + -0.9583333335) equal to 1.443976954 and -1.443976954.

Subproblem 1
y + -0.9583333335 = 1.443976954

Simplifying
y + -0.9583333335 = 1.443976954

Reorder the terms:
-0.9583333335 + y = 1.443976954

Solving
-0.9583333335 + y = 1.443976954

Solving for variable 'y'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + y = 1.443976954 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + y = 1.443976954 + 0.9583333335
y = 1.443976954 + 0.9583333335

Combine like terms: 1.443976954 + 0.9583333335 = 2.4023102875
y = 2.4023102875

Simplifying
y = 2.4023102875

Subproblem 2
y + -0.9583333335 = -1.443976954

Simplifying
y + -0.9583333335 = -1.443976954

Reorder the terms:
-0.9583333335 + y = -1.443976954

Solving
-0.9583333335 + y = -1.443976954

Solving for variable 'y'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + y = -1.443976954 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + y = -1.443976954 + 0.9583333335
y = -1.443976954 + 0.9583333335

Combine like terms: -1.443976954 + 0.9583333335 = -0.4856436205
y = -0.4856436205

Simplifying
y = -0.4856436205

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.4023102875, -0.4856436205}
Solution
y = {2.4023102875, -0.4856436205}