4r(7r+3)=0

Solution for 4r(7r+3)=0 equation:

Simplifying
4r(7r + 3) = 0

Reorder the terms:
4r(3 + 7r) = 0
(3 * 4r + 7r * 4r) = 0
(12r + 28r2) = 0

Solving
12r + 28r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r'.
4r(3 + 7r) = 0

Ignore the factor 4.
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 '(3 + 7r)' equal to zero and attempt to solve:

Simplifying
3 + 7r = 0

Solving
3 + 7r = 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 + 7r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7r = 0 + -3
7r = 0 + -3

Combine like terms: 0 + -3 = -3
7r = -3

Divide each side by '7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Solution
r = {0, -0.4285714286}