y^2+24y-60=0

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Solution for y^2+24y-60=0 equation: 


Simplifying
y2 + 24y + -60 = 0

Reorder the terms:
-60 + 24y + y2 = 0

Solving
-60 + 24y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 24y + 60 + y2 = 0 + 60

Reorder the terms:
-60 + 60 + 24y + y2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 24y + y2 = 0 + 60
24y + y2 = 0 + 60

Combine like terms: 0 + 60 = 60
24y + y2 = 60

The y term is 24y.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24y + 144 + y2 = 60 + 144

Reorder the terms:
144 + 24y + y2 = 60 + 144

Combine like terms: 60 + 144 = 204
144 + 24y + y2 = 204

Factor a perfect square on the left side:
(y + 12)(y + 12) = 204

Calculate the square root of the right side: 14.282856857

Break this problem into two subproblems by setting 
(y + 12) equal to 14.282856857 and -14.282856857.


Subproblem 1
y + 12 = 14.282856857

Simplifying
y + 12 = 14.282856857

Reorder the terms:
12 + y = 14.282856857

Solving
12 + y = 14.282856857

Solving for variable 'y'.

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

Add '-12' to each side of the equation.
12 + -12 + y = 14.282856857 + -12

Combine like terms: 12 + -12 = 0
0 + y = 14.282856857 + -12
y = 14.282856857 + -12

Combine like terms: 14.282856857 + -12 = 2.282856857
y = 2.282856857

Simplifying
y = 2.282856857


Subproblem 2
y + 12 = -14.282856857

Simplifying
y + 12 = -14.282856857

Reorder the terms:
12 + y = -14.282856857

Solving
12 + y = -14.282856857

Solving for variable 'y'.

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

Add '-12' to each side of the equation.
12 + -12 + y = -14.282856857 + -12

Combine like terms: 12 + -12 = 0
0 + y = -14.282856857 + -12
y = -14.282856857 + -12

Combine like terms: -14.282856857 + -12 = -26.282856857
y = -26.282856857

Simplifying
y = -26.282856857


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.282856857, -26.282856857}

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