(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 = 5r
(-3 + 5r + 12r2) = 0

Solving
-3 + 5r + 12r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-0.75, 0.3333333333}