2(r+2)(r+2)=72

Solution for 2(r+2)(r+2)=72 equation:

Simplifying
2(r + 2)(r + 2) = 72

Reorder the terms:
2(2 + r)(r + 2) = 72

Reorder the terms:
2(2 + r)(2 + r) = 72

Multiply (2 + r) * (2 + r)
2(2(2 + r) + r(2 + r)) = 72
2((2 * 2 + r * 2) + r(2 + r)) = 72
2((4 + 2r) + r(2 + r)) = 72
2(4 + 2r + (2 * r + r * r)) = 72
2(4 + 2r + (2r + r2)) = 72

Combine like terms: 2r + 2r = 4r
2(4 + 4r + r2) = 72
(4 * 2 + 4r * 2 + r2 * 2) = 72
(8 + 8r + 2r2) = 72

Solving
8 + 8r + 2r2 = 72

Solving for variable 'r'.

Reorder the terms:
8 + -72 + 8r + 2r2 = 72 + -72

Combine like terms: 8 + -72 = -64
-64 + 8r + 2r2 = 72 + -72

Combine like terms: 72 + -72 = 0
-64 + 8r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + 4r + r2) = 0

Factor a trinomial.
2((-8 + -1r)(4 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1r)' equal to zero and attempt to solve:

Simplifying
-8 + -1r = 0

Solving
-8 + -1r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1r = 0 + 8
-1r = 0 + 8

Combine like terms: 0 + 8 = 8
-1r = 8

Divide each side by '-1'.
r = -8

Simplifying
r = -8
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-8, 4}