(r-3)(r+6)=64

Solution for (r-3)(r+6)=64 equation:

Simplifying
(r + -3)(r + 6) = 64

Reorder the terms:
(-3 + r)(r + 6) = 64

Reorder the terms:
(-3 + r)(6 + r) = 64

Multiply (-3 + r) * (6 + r)
(-3(6 + r) + r(6 + r)) = 64
((6 * -3 + r * -3) + r(6 + r)) = 64
((-18 + -3r) + r(6 + r)) = 64
(-18 + -3r + (6 * r + r * r)) = 64
(-18 + -3r + (6r + r2)) = 64

Combine like terms: -3r + 6r = 3r
(-18 + 3r + r2) = 64

Solving
-18 + 3r + r2 = 64

Solving for variable 'r'.

Reorder the terms:
-18 + -64 + 3r + r2 = 64 + -64

Combine like terms: -18 + -64 = -82
-82 + 3r + r2 = 64 + -64

Combine like terms: 64 + -64 = 0
-82 + 3r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + 3r + 82 + r2 = 0 + 82

Reorder the terms:
-82 + 82 + 3r + r2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 3r + r2 = 0 + 82
3r + r2 = 0 + 82

Combine like terms: 0 + 82 = 82
3r + r2 = 82

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 82 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 82 + 2.25

Combine like terms: 82 + 2.25 = 84.25
2.25 + 3r + r2 = 84.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(r + 1.5) equal to 9.178779875 and -9.178779875.

Subproblem 1
r + 1.5 = 9.178779875

Simplifying
r + 1.5 = 9.178779875

Reorder the terms:
1.5 + r = 9.178779875

Solving
1.5 + r = 9.178779875

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 9.178779875 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 9.178779875 + -1.5
r = 9.178779875 + -1.5

Combine like terms: 9.178779875 + -1.5 = 7.678779875
r = 7.678779875

Simplifying
r = 7.678779875

Subproblem 2
r + 1.5 = -9.178779875

Simplifying
r + 1.5 = -9.178779875

Reorder the terms:
1.5 + r = -9.178779875

Solving
1.5 + r = -9.178779875

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -9.178779875 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -9.178779875 + -1.5
r = -9.178779875 + -1.5

Combine like terms: -9.178779875 + -1.5 = -10.678779875
r = -10.678779875

Simplifying
r = -10.678779875

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {7.678779875, -10.678779875}