(4r-8)(4r-8)=16

Solution for (4r-8)(4r-8)=16 equation:

Simplifying
(4r + -8)(4r + -8) = 16

Reorder the terms:
(-8 + 4r)(4r + -8) = 16

Reorder the terms:
(-8 + 4r)(-8 + 4r) = 16

Multiply (-8 + 4r) * (-8 + 4r)
(-8(-8 + 4r) + 4r * (-8 + 4r)) = 16
((-8 * -8 + 4r * -8) + 4r * (-8 + 4r)) = 16
((64 + -32r) + 4r * (-8 + 4r)) = 16
(64 + -32r + (-8 * 4r + 4r * 4r)) = 16
(64 + -32r + (-32r + 16r2)) = 16

Combine like terms: -32r + -32r = -64r
(64 + -64r + 16r2) = 16

Solving
64 + -64r + 16r2 = 16

Solving for variable 'r'.

Reorder the terms:
64 + -16 + -64r + 16r2 = 16 + -16

Combine like terms: 64 + -16 = 48
48 + -64r + 16r2 = 16 + -16

Combine like terms: 16 + -16 = 0
48 + -64r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(3 + -4r + r2) = 0

Factor a trinomial.
16((1 + -1r)(3 + -1r)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {1, 3}