r(13r+3)=10

Solution for r(13r+3)=10 equation:

Simplifying
r(13r + 3) = 10

Reorder the terms:
r(3 + 13r) = 10
(3 * r + 13r * r) = 10
(3r + 13r2) = 10

Solving
3r + 13r2 = 10

Solving for variable 'r'.

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

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

Factor a trinomial.
(-1 + -1r)(10 + -13r) = 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 '(10 + -13r)' equal to zero and attempt to solve:

Simplifying
10 + -13r = 0

Solving
10 + -13r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -13r = 0 + -10

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

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

Divide each side by '-13'.
r = 0.7692307692

Simplifying
r = 0.7692307692
Solution
r = {-1, 0.7692307692}