2r^2-39r+145=0

Solution for 2r^2-39r+145=0 equation:

Simplifying
2r2 + -39r + 145 = 0

Reorder the terms:
145 + -39r + 2r2 = 0

Solving
145 + -39r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -1r)(29 + -2r) = 0

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

Simplifying
5 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Subproblem 2
Set the factor '(29 + -2r)' equal to zero and attempt to solve:

Simplifying
29 + -2r = 0

Solving
29 + -2r = 0

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

Add '-29' to each side of the equation.
29 + -29 + -2r = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -2r = 0 + -29
-2r = 0 + -29

Combine like terms: 0 + -29 = -29
-2r = -29

Divide each side by '-2'.
r = 14.5

Simplifying
r = 14.5
Solution
r = {5, 14.5}