(8r+5)(3r-4)=0

Solution for (8r+5)(3r-4)=0 equation:

Simplifying
(8r + 5)(3r + -4) = 0

Reorder the terms:
(5 + 8r)(3r + -4) = 0

Reorder the terms:
(5 + 8r)(-4 + 3r) = 0

Multiply (5 + 8r) * (-4 + 3r)
(5(-4 + 3r) + 8r * (-4 + 3r)) = 0
((-4 * 5 + 3r * 5) + 8r * (-4 + 3r)) = 0
((-20 + 15r) + 8r * (-4 + 3r)) = 0
(-20 + 15r + (-4 * 8r + 3r * 8r)) = 0
(-20 + 15r + (-32r + 24r2)) = 0

Combine like terms: 15r + -32r = -17r
(-20 + -17r + 24r2) = 0

Solving
-20 + -17r + 24r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -8r)(4 + -3r) = 0

Subproblem 1
Set the factor '(-5 + -8r)' equal to zero and attempt to solve:

Simplifying
-5 + -8r = 0

Solving
-5 + -8r = 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 + -8r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8r = 0 + 5
-8r = 0 + 5

Combine like terms: 0 + 5 = 5
-8r = 5

Divide each side by '-8'.
r = -0.625

Simplifying
r = -0.625
Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve:

Simplifying
4 + -3r = 0

Solving
4 + -3r = 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 + -3r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3r = 0 + -4
-3r = 0 + -4

Combine like terms: 0 + -4 = -4
-3r = -4

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Solution
r = {-0.625, 1.333333333}