2r(r+3)(5r-4)=0

Solution for 2r(r+3)(5r-4)=0 equation:

Simplifying
2r(r + 3)(5r + -4) = 0

Reorder the terms:
2r(3 + r)(5r + -4) = 0

Reorder the terms:
2r(3 + r)(-4 + 5r) = 0

Multiply (3 + r) * (-4 + 5r)
2r(3(-4 + 5r) + r(-4 + 5r)) = 0
2r((-4 * 3 + 5r * 3) + r(-4 + 5r)) = 0
2r((-12 + 15r) + r(-4 + 5r)) = 0
2r(-12 + 15r + (-4 * r + 5r * r)) = 0
2r(-12 + 15r + (-4r + 5r2)) = 0

Combine like terms: 15r + -4r = 11r
2r(-12 + 11r + 5r2) = 0
(-12 * 2r + 11r * 2r + 5r2 * 2r) = 0
(-24r + 22r2 + 10r3) = 0

Solving
-24r + 22r2 + 10r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-12 + 11r + 5r2) = 0

Factor a trinomial.
2r((-3 + -1r)(4 + -5r)) = 0

Ignore the factor 2.
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 + -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
Subproblem 3
Set the factor '(4 + -5r)' equal to zero and attempt to solve:

Simplifying
4 + -5r = 0

Solving
4 + -5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5r = 0 + -4
-5r = 0 + -4

Combine like terms: 0 + -4 = -4
-5r = -4

Divide each side by '-5'.
r = 0.8

Simplifying
r = 0.8
Solution
r = {0, -3, 0.8}