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

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

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

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

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

Multiply (-1 + 5r) * (1 + 3r)
(-1(1 + 3r) + 5r * (1 + 3r)) = 0
((1 * -1 + 3r * -1) + 5r * (1 + 3r)) = 0
((-1 + -3r) + 5r * (1 + 3r)) = 0
(-1 + -3r + (1 * 5r + 3r * 5r)) = 0
(-1 + -3r + (5r + 15r2)) = 0

Combine like terms: -3r + 5r = 2r
(-1 + 2r + 15r2) = 0

Solving
-1 + 2r + 15r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-1 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

Solving
1 + -5r = 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 + -5r = 0 + -1

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

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

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-0.3333333333, 0.2}