r^2-6r=55

Solution for r^2-6r=55 equation:

Simplifying
r2 + -6r = 55

Reorder the terms:
-6r + r2 = 55

Solving
-6r + r2 = 55

Solving for variable 'r'.

Reorder the terms:
-55 + -6r + r2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + -6r + r2 = 0

Factor a trinomial.
(-5 + -1r)(11 + -1r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 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 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(11 + -1r)' equal to zero and attempt to solve:

Simplifying
11 + -1r = 0

Solving
11 + -1r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1r = 0 + -11
-1r = 0 + -11

Combine like terms: 0 + -11 = -11
-1r = -11

Divide each side by '-1'.
r = 11

Simplifying
r = 11
Solution
r = {-5, 11}