8r[4r-(1r+6t)]=

Solution for 8r[4r-(1r+6t)]= equation:

Simplifying
8r[4r + -1(1r + 6t)] = 0
8r[4r + (1r * -1 + 6t * -1)] = 0
8r[4r + (-1r + -6t)] = 0

Combine like terms: 4r + -1r = 3r
8r[3r + -6t] = 0
[3r * 8r + -6t * 8r] = 0

Reorder the terms:
[-48rt + 24r2] = 0
[-48rt + 24r2] = 0

Solving
-48rt + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '24r'.
24r(-2t + r) = 0

Ignore the factor 24.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-2t + r)' equal to zero and attempt to solve:

Simplifying
-2t + r = 0

Reorder the terms:
r + -2t = 0

Solving
r + -2t = 0

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

Add '2t' to each side of the equation.
r + -2t + 2t = 0 + 2t

Combine like terms: -2t + 2t = 0
r + 0 = 0 + 2t
r = 0 + 2t
Remove the zero:
r = 2t

Simplifying
r = 2t
Solution
r = {0, 2t}