3r(5r+2)(r-3)=0

Solution for 3r(5r+2)(r-3)=0 equation:

Simplifying
3r(5r + 2)(r + -3) = 0

Reorder the terms:
3r(2 + 5r)(r + -3) = 0

Reorder the terms:
3r(2 + 5r)(-3 + r) = 0

Multiply (2 + 5r) * (-3 + r)
3r(2(-3 + r) + 5r * (-3 + r)) = 0
3r((-3 * 2 + r * 2) + 5r * (-3 + r)) = 0
3r((-6 + 2r) + 5r * (-3 + r)) = 0
3r(-6 + 2r + (-3 * 5r + r * 5r)) = 0
3r(-6 + 2r + (-15r + 5r2)) = 0

Combine like terms: 2r + -15r = -13r
3r(-6 + -13r + 5r2) = 0
(-6 * 3r + -13r * 3r + 5r2 * 3r) = 0
(-18r + -39r2 + 15r3) = 0

Solving
-18r + -39r2 + 15r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-6 + -13r + 5r2) = 0

Factor a trinomial.
3r((-2 + -5r)(3 + -1r)) = 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 '(-2 + -5r)' equal to zero and attempt to solve:

Simplifying
-2 + -5r = 0

Solving
-2 + -5r = 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 + -5r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5r = 0 + 2
-5r = 0 + 2

Combine like terms: 0 + 2 = 2
-5r = 2

Divide each side by '-5'.
r = -0.4

Simplifying
r = -0.4
Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0, -0.4, 3}