2r^2-5r-102=0

Solution for 2r^2-5r-102=0 equation:

Simplifying
2r2 + -5r + -102 = 0

Reorder the terms:
-102 + -5r + 2r2 = 0

Solving
-102 + -5r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-6 + -1r)(17 + -2r) = 0

Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve:

Simplifying
-6 + -1r = 0

Solving
-6 + -1r = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1r = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 0 + 6
-1r = 0 + 6

Combine like terms: 0 + 6 = 6
-1r = 6

Divide each side by '-1'.
r = -6

Simplifying
r = -6
Subproblem 2
Set the factor '(17 + -2r)' equal to zero and attempt to solve:

Simplifying
17 + -2r = 0

Solving
17 + -2r = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2r = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2r = 0 + -17
-2r = 0 + -17

Combine like terms: 0 + -17 = -17
-2r = -17

Divide each side by '-2'.
r = 8.5

Simplifying
r = 8.5
Solution
r = {-6, 8.5}