4r(6r+3)=

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

Simplifying
4r(6r + 3) = 0

Reorder the terms:
4r(3 + 6r) = 0
(3 * 4r + 6r * 4r) = 0
(12r + 24r2) = 0

Solving
12r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '12r'.
12r(1 + 2r) = 0

Ignore the factor 12.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
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
Solution
r = {0, -0.5}