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

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

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

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

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

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

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

Solving
-5 + 2r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -3r)(1 + -1r) = 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 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-1.666666667, 1}