(8r-3)(r-6)=0

Solution for (8r-3)(r-6)=0 equation:

Simplifying
(8r + -3)(r + -6) = 0

Reorder the terms:
(-3 + 8r)(r + -6) = 0

Reorder the terms:
(-3 + 8r)(-6 + r) = 0

Multiply (-3 + 8r) * (-6 + r)
(-3(-6 + r) + 8r * (-6 + r)) = 0
((-6 * -3 + r * -3) + 8r * (-6 + r)) = 0
((18 + -3r) + 8r * (-6 + r)) = 0
(18 + -3r + (-6 * 8r + r * 8r)) = 0
(18 + -3r + (-48r + 8r2)) = 0

Combine like terms: -3r + -48r = -51r
(18 + -51r + 8r2) = 0

Solving
18 + -51r + 8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -8r)(6 + -1r) = 0

Subproblem 1
Set the factor '(3 + -8r)' equal to zero and attempt to solve:

Simplifying
3 + -8r = 0

Solving
3 + -8r = 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 + -8r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8r = 0 + -3
-8r = 0 + -3

Combine like terms: 0 + -3 = -3
-8r = -3

Divide each side by '-8'.
r = 0.375

Simplifying
r = 0.375
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {0.375, 6}