24-6r=6r(4-r)

Solution for 24-6r=6r(4-r) equation:

Simplifying
24 + -6r = 6r(4 + -1r)
24 + -6r = (4 * 6r + -1r * 6r)
24 + -6r = (24r + -6r2)

Solving
24 + -6r = 24r + -6r2

Solving for variable 'r'.

Combine like terms: -6r + -24r = -30r
24 + -30r + 6r2 = 24r + -6r2 + -24r + 6r2

Reorder the terms:
24 + -30r + 6r2 = 24r + -24r + -6r2 + 6r2

Combine like terms: 24r + -24r = 0
24 + -30r + 6r2 = 0 + -6r2 + 6r2
24 + -30r + 6r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
24 + -30r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -5r + r2) = 0

Factor a trinomial.
6((1 + -1r)(4 + -1r)) = 0

Ignore the factor 6.
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 '(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 = {1, 4}