(4r-1)(3r+5)=0

Solution for (4r-1)(3r+5)=0 equation:

Simplifying
(4r + -1)(3r + 5) = 0

Reorder the terms:
(-1 + 4r)(3r + 5) = 0

Reorder the terms:
(-1 + 4r)(5 + 3r) = 0

Multiply (-1 + 4r) * (5 + 3r)
(-1(5 + 3r) + 4r * (5 + 3r)) = 0
((5 * -1 + 3r * -1) + 4r * (5 + 3r)) = 0
((-5 + -3r) + 4r * (5 + 3r)) = 0
(-5 + -3r + (5 * 4r + 3r * 4r)) = 0
(-5 + -3r + (20r + 12r2)) = 0

Combine like terms: -3r + 20r = 17r
(-5 + 17r + 12r2) = 0

Solving
-5 + 17r + 12r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-5 + -3r)' equal to zero and attempt to solve:

Simplifying
-5 + -3r = 0

Solving
-5 + -3r = 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 + -3r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3r = 0 + 5
-3r = 0 + 5

Combine like terms: 0 + 5 = 5
-3r = 5

Divide each side by '-3'.
r = -1.666666667

Simplifying
r = -1.666666667
Subproblem 2
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Solution
r = {-1.666666667, 0.25}