3r^2-13r=10

Solution for 3r^2-13r=10 equation:

Simplifying
3r2 + -13r = 10

Reorder the terms:
-13r + 3r2 = 10

Solving
-13r + 3r2 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + -13r + 3r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -13r + 3r2 = 0

Factor a trinomial.
(-2 + -3r)(5 + -1r) = 0

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

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 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 + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3r = 0 + 2
-3r = 0 + 2

Combine like terms: 0 + 2 = 2
-3r = 2

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Subproblem 2
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
Solution
r = {-0.6666666667, 5}