15r^2-7r-2=0

Solution for 15r^2-7r-2=0 equation:

Simplifying
15r2 + -7r + -2 = 0

Reorder the terms:
-2 + -7r + 15r2 = 0

Solving
-2 + -7r + 15r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {-0.2, 0.6666666667}