r^2=7r-6

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

Simplifying
r2 = 7r + -6

Reorder the terms:
r2 = -6 + 7r

Solving
r2 = -6 + 7r

Solving for variable 'r'.

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

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

Combine like terms: -6 + 6 = 0
6 + -7r + r2 = 0 + 7r + -7r
6 + -7r + r2 = 7r + -7r

Combine like terms: 7r + -7r = 0
6 + -7r + r2 = 0

Factor a trinomial.
(1 + -1r)(6 + -1r) = 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 '(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 = {1, 6}