6(4r-3)(r+5)=0

Solution for 6(4r-3)(r+5)=0 equation:

Simplifying
6(4r + -3)(r + 5) = 0

Reorder the terms:
6(-3 + 4r)(r + 5) = 0

Reorder the terms:
6(-3 + 4r)(5 + r) = 0

Multiply (-3 + 4r) * (5 + r)
6(-3(5 + r) + 4r * (5 + r)) = 0
6((5 * -3 + r * -3) + 4r * (5 + r)) = 0
6((-15 + -3r) + 4r * (5 + r)) = 0
6(-15 + -3r + (5 * 4r + r * 4r)) = 0
6(-15 + -3r + (20r + 4r2)) = 0

Combine like terms: -3r + 20r = 17r
6(-15 + 17r + 4r2) = 0
(-15 * 6 + 17r * 6 + 4r2 * 6) = 0
(-90 + 102r + 24r2) = 0

Solving
-90 + 102r + 24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + 17r + 4r2) = 0

Factor a trinomial.
6((-5 + -1r)(3 + -4r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
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 = {-5, 0.75}