5r^2-13r=-6

Solution for 5r^2-13r=-6 equation:

Simplifying
5r2 + -13r = -6

Reorder the terms:
-13r + 5r2 = -6

Solving
-13r + 5r2 = -6

Solving for variable 'r'.

Reorder the terms:
6 + -13r + 5r2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -13r + 5r2 = 0

Factor a trinomial.
(3 + -5r)(2 + -1r) = 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 '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0.6, 2}