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

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

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

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

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

Multiply (-3 + 6r) * (-3 + 8r)
(-3(-3 + 8r) + 6r * (-3 + 8r)) = 0
((-3 * -3 + 8r * -3) + 6r * (-3 + 8r)) = 0
((9 + -24r) + 6r * (-3 + 8r)) = 0
(9 + -24r + (-3 * 6r + 8r * 6r)) = 0
(9 + -24r + (-18r + 48r2)) = 0

Combine like terms: -24r + -18r = -42r
(9 + -42r + 48r2) = 0

Solving
9 + -42r + 48r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -14r + 16r2) = 0

Factor a trinomial.
3((3 + -8r)(1 + -2r)) = 0

Ignore the factor 3.
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 '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {0.375, 0.5}