-7r^2-r+6=0

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

Simplifying
-7r2 + -1r + 6 = 0

Reorder the terms:
6 + -1r + -7r2 = 0

Solving
6 + -1r + -7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(6 + -7r)(1 + r) = 0

Subproblem 1
Set the factor '(6 + -7r)' equal to zero and attempt to solve:

Simplifying
6 + -7r = 0

Solving
6 + -7r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7r = 0 + -6
-7r = 0 + -6

Combine like terms: 0 + -6 = -6
-7r = -6

Divide each side by '-7'.
r = 0.8571428571

Simplifying
r = 0.8571428571
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

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

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

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

Simplifying
r = -1
Solution
r = {0.8571428571, -1}