3r(4r-3)=0

Solution for 3r(4r-3)=0 equation:

Simplifying
3r(4r + -3) = 0

Reorder the terms:
3r(-3 + 4r) = 0
(-3 * 3r + 4r * 3r) = 0
(-9r + 12r2) = 0

Solving
-9r + 12r2 = 0

Solving for variable 'r'.

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

Ignore the factor 3.
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 + 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
Solution
r = {0, 0.75}