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

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

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

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

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

Multiply (2 + 4r) * (1 + 3r)
(2(1 + 3r) + 4r * (1 + 3r)) = 0
((1 * 2 + 3r * 2) + 4r * (1 + 3r)) = 0
((2 + 6r) + 4r * (1 + 3r)) = 0
(2 + 6r + (1 * 4r + 3r * 4r)) = 0
(2 + 6r + (4r + 12r2)) = 0

Combine like terms: 6r + 4r = 10r
(2 + 10r + 12r2) = 0

Solving
2 + 10r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 5r + 6r2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {-0.5, -0.3333333333}