-6r^2-r+7=0

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

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

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

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

Solving for variable 'r'.

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

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

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Subproblem 2
Set the factor '(7 + 6r)' equal to zero and attempt to solve:

Simplifying
7 + 6r = 0

Solving
7 + 6r = 0

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

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

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

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

Divide each side by '6'.
r = -1.166666667

Simplifying
r = -1.166666667
Solution
r = {1, -1.166666667}