7r^2-41r-6=0

Solution for 7r^2-41r-6=0 equation:

Simplifying
7r2 + -41r + -6 = 0

Reorder the terms:
-6 + -41r + 7r2 = 0

Solving
-6 + -41r + 7r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-1 + -7r = 0

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

Combine like terms: -1 + 1 = 0
0 + -7r = 0 + 1
-7r = 0 + 1

Combine like terms: 0 + 1 = 1
-7r = 1

Divide each side by '-7'.
r = -0.1428571429

Simplifying
r = -0.1428571429
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

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

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-0.1428571429, 6}