(3r+2)(4r+1)=0

Solution for (3r+2)(4r+1)=0 equation:

Simplifying
(3r + 2)(4r + 1) = 0

Reorder the terms:
(2 + 3r)(4r + 1) = 0

Reorder the terms:
(2 + 3r)(1 + 4r) = 0

Multiply (2 + 3r) * (1 + 4r)
(2(1 + 4r) + 3r * (1 + 4r)) = 0
((1 * 2 + 4r * 2) + 3r * (1 + 4r)) = 0
((2 + 8r) + 3r * (1 + 4r)) = 0
(2 + 8r + (1 * 3r + 4r * 3r)) = 0
(2 + 8r + (3r + 12r2)) = 0

Combine like terms: 8r + 3r = 11r
(2 + 11r + 12r2) = 0

Solving
2 + 11r + 12r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + 3r)(1 + 4r) = 0

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

Simplifying
2 + 3r = 0

Solving
2 + 3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3r = 0 + -2

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

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

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Subproblem 2
Set the factor '(1 + 4r)' equal to zero and attempt to solve:

Simplifying
1 + 4r = 0

Solving
1 + 4r = 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 + 4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4r = 0 + -1
4r = 0 + -1

Combine like terms: 0 + -1 = -1
4r = -1

Divide each side by '4'.
r = -0.25

Simplifying
r = -0.25
Solution
r = {-0.6666666667, -0.25}