(3r-1)(4r-3)=0

Solution for (3r-1)(4r-3)=0 equation:

Simplifying
(3r + -1)(4r + -3) = 0

Reorder the terms:
(-1 + 3r)(4r + -3) = 0

Reorder the terms:
(-1 + 3r)(-3 + 4r) = 0

Multiply (-1 + 3r) * (-3 + 4r)
(-1(-3 + 4r) + 3r * (-3 + 4r)) = 0
((-3 * -1 + 4r * -1) + 3r * (-3 + 4r)) = 0
((3 + -4r) + 3r * (-3 + 4r)) = 0
(3 + -4r + (-3 * 3r + 4r * 3r)) = 0
(3 + -4r + (-9r + 12r2)) = 0

Combine like terms: -4r + -9r = -13r
(3 + -13r + 12r2) = 0

Solving
3 + -13r + 12r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -3r)(3 + -4r) = 0

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

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 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 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Solution
r = {0.3333333333, 0.75}