4r(r-1)=(8-r)(8+r)

Solution for 4r(r-1)=(8-r)(8+r) equation:

Simplifying
4r(r + -1) = (8 + -1r)(8 + r)

Reorder the terms:
4r(-1 + r) = (8 + -1r)(8 + r)
(-1 * 4r + r * 4r) = (8 + -1r)(8 + r)
(-4r + 4r2) = (8 + -1r)(8 + r)

Multiply (8 + -1r) * (8 + r)
-4r + 4r2 = (8(8 + r) + -1r * (8 + r))
-4r + 4r2 = ((8 * 8 + r * 8) + -1r * (8 + r))
-4r + 4r2 = ((64 + 8r) + -1r * (8 + r))
-4r + 4r2 = (64 + 8r + (8 * -1r + r * -1r))
-4r + 4r2 = (64 + 8r + (-8r + -1r2))

Combine like terms: 8r + -8r = 0
-4r + 4r2 = (64 + 0 + -1r2)
-4r + 4r2 = (64 + -1r2)

Solving
-4r + 4r2 = 64 + -1r2

Solving for variable 'r'.

Reorder the terms:
-64 + -4r + 4r2 + r2 = 64 + -1r2 + -64 + r2

Combine like terms: 4r2 + r2 = 5r2
-64 + -4r + 5r2 = 64 + -1r2 + -64 + r2

Reorder the terms:
-64 + -4r + 5r2 = 64 + -64 + -1r2 + r2

Combine like terms: 64 + -64 = 0
-64 + -4r + 5r2 = 0 + -1r2 + r2
-64 + -4r + 5r2 = -1r2 + r2

Combine like terms: -1r2 + r2 = 0
-64 + -4r + 5r2 = 0

Factor a trinomial.
(-16 + -5r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -5r)' equal to zero and attempt to solve:

Simplifying
-16 + -5r = 0

Solving
-16 + -5r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5r = 0 + 16
-5r = 0 + 16

Combine like terms: 0 + 16 = 16
-5r = 16

Divide each side by '-5'.
r = -3.2

Simplifying
r = -3.2
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 = {-3.2, 4}