(2r-1)(5r+3)=

Solution for (2r-1)(5r+3)= equation:

Simplifying
(2r + -1)(5r + 3) = 0

Reorder the terms:
(-1 + 2r)(5r + 3) = 0

Reorder the terms:
(-1 + 2r)(3 + 5r) = 0

Multiply (-1 + 2r) * (3 + 5r)
(-1(3 + 5r) + 2r * (3 + 5r)) = 0
((3 * -1 + 5r * -1) + 2r * (3 + 5r)) = 0
((-3 + -5r) + 2r * (3 + 5r)) = 0
(-3 + -5r + (3 * 2r + 5r * 2r)) = 0
(-3 + -5r + (6r + 10r2)) = 0

Combine like terms: -5r + 6r = 1r
(-3 + 1r + 10r2) = 0

Solving
-3 + 1r + 10r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-3 + -5r = 0

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

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

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

Divide each side by '-5'.
r = -0.6

Simplifying
r = -0.6
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-0.6, 0.5}