6r^2+7r-5=0

Solution for 6r^2+7r-5=0 equation:

Simplifying
6r2 + 7r + -5 = 0

Reorder the terms:
-5 + 7r + 6r2 = 0

Solving
-5 + 7r + 6r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(-5 + -3r)' equal to zero and attempt to solve:

Simplifying
-5 + -3r = 0

Solving
-5 + -3r = 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 + -3r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3r = 0 + 5
-3r = 0 + 5

Combine like terms: 0 + 5 = 5
-3r = 5

Divide each side by '-3'.
r = -1.666666667

Simplifying
r = -1.666666667
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2r = 0 + -1
-2r = 0 + -1

Combine like terms: 0 + -1 = -1
-2r = -1

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-1.666666667, 0.5}