64=y(y+13)

Solution for 64=y(y+13) equation:

Simplifying
64 = y(y + 13)

Reorder the terms:
64 = y(13 + y)
64 = (13 * y + y * y)
64 = (13y + y2)

Solving
64 = 13y + y2

Solving for variable 'y'.

Reorder the terms:
64 + -13y + -1y2 = 13y + -13y + y2 + -1y2

Combine like terms: 13y + -13y = 0
64 + -13y + -1y2 = 0 + y2 + -1y2
64 + -13y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
64 + -13y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-64 + 13y + y2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 13y + 64 + y2 = 0 + 64

Reorder the terms:
-64 + 64 + 13y + y2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 13y + y2 = 0 + 64
13y + y2 = 0 + 64

Combine like terms: 0 + 64 = 64
13y + y2 = 64

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = 64 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 64 + 42.25

Combine like terms: 64 + 42.25 = 106.25
42.25 + 13y + y2 = 106.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(y + 6.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
y + 6.5 = 10.307764064

Simplifying
y + 6.5 = 10.307764064

Reorder the terms:
6.5 + y = 10.307764064

Solving
6.5 + y = 10.307764064

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 10.307764064 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 10.307764064 + -6.5
y = 10.307764064 + -6.5

Combine like terms: 10.307764064 + -6.5 = 3.807764064
y = 3.807764064

Simplifying
y = 3.807764064

Subproblem 2
y + 6.5 = -10.307764064

Simplifying
y + 6.5 = -10.307764064

Reorder the terms:
6.5 + y = -10.307764064

Solving
6.5 + y = -10.307764064

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = -10.307764064 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -10.307764064 + -6.5
y = -10.307764064 + -6.5

Combine like terms: -10.307764064 + -6.5 = -16.807764064
y = -16.807764064

Simplifying
y = -16.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.807764064, -16.807764064}