10r^2+13r-3=0

Solution for 10r^2+13r-3=0 equation:

Simplifying
10r2 + 13r + -3 = 0

Reorder the terms:
-3 + 13r + 10r2 = 0

Solving
-3 + 13r + 10r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-3 + -2r = 0

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

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

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

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
Subproblem 2
Set the factor '(1 + -5r)' equal to zero and attempt to solve:

Simplifying
1 + -5r = 0

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

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

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

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-1.5, 0.2}