5r^2+17r-12=0

Solution for 5r^2+17r-12=0 equation:

Simplifying
5r2 + 17r + -12 = 0

Reorder the terms:
-12 + 17r + 5r2 = 0

Solving
-12 + 17r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -1r)(3 + -5r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
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
Solution
r = {-4, 0.6}