3r^2-5r-8=0

Solution for 3r^2-5r-8=0 equation:

Simplifying
3r2 + -5r + -8 = 0

Reorder the terms:
-8 + -5r + 3r2 = 0

Solving
-8 + -5r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -1r)(8 + -3r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -3r)' equal to zero and attempt to solve:

Simplifying
8 + -3r = 0

Solving
8 + -3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3r = 0 + -8
-3r = 0 + -8

Combine like terms: 0 + -8 = -8
-3r = -8

Divide each side by '-3'.
r = 2.666666667

Simplifying
r = 2.666666667
Solution
r = {-1, 2.666666667}