(6+r)(6+r)=r^2+81

Solution for (6+r)(6+r)=r^2+81 equation:

Simplifying
(6 + r)(6 + r) = r2 + 81

Multiply (6 + r) * (6 + r)
(6(6 + r) + r(6 + r)) = r2 + 81
((6 * 6 + r * 6) + r(6 + r)) = r2 + 81
((36 + 6r) + r(6 + r)) = r2 + 81
(36 + 6r + (6 * r + r * r)) = r2 + 81
(36 + 6r + (6r + r2)) = r2 + 81

Combine like terms: 6r + 6r = 12r
(36 + 12r + r2) = r2 + 81

Reorder the terms:
36 + 12r + r2 = 81 + r2

Add '-1r2' to each side of the equation.
36 + 12r + r2 + -1r2 = 81 + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
36 + 12r + 0 = 81 + r2 + -1r2
36 + 12r = 81 + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
36 + 12r = 81 + 0
36 + 12r = 81

Solving
36 + 12r = 81

Solving for variable 'r'.

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

Add '-36' to each side of the equation.
36 + -36 + 12r = 81 + -36

Combine like terms: 36 + -36 = 0
0 + 12r = 81 + -36
12r = 81 + -36

Combine like terms: 81 + -36 = 45
12r = 45

Divide each side by '12'.
r = 3.75

Simplifying
r = 3.75