(3r-4)(4r-6)=

Solution for (3r-4)(4r-6)= equation:

Simplifying
(3r + -4)(4r + -6) = 0

Reorder the terms:
(-4 + 3r)(4r + -6) = 0

Reorder the terms:
(-4 + 3r)(-6 + 4r) = 0

Multiply (-4 + 3r) * (-6 + 4r)
(-4(-6 + 4r) + 3r * (-6 + 4r)) = 0
((-6 * -4 + 4r * -4) + 3r * (-6 + 4r)) = 0
((24 + -16r) + 3r * (-6 + 4r)) = 0
(24 + -16r + (-6 * 3r + 4r * 3r)) = 0
(24 + -16r + (-18r + 12r2)) = 0

Combine like terms: -16r + -18r = -34r
(24 + -34r + 12r2) = 0

Solving
24 + -34r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -17r + 6r2) = 0

Factor a trinomial.
2((4 + -3r)(3 + -2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -3r)' equal to zero and attempt to solve:

Simplifying
4 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {1.333333333, 1.5}