r(r-6)=7

Solution for r(r-6)=7 equation:

Simplifying
r(r + -6) = 7

Reorder the terms:
r(-6 + r) = 7
(-6 * r + r * r) = 7
(-6r + r2) = 7

Solving
-6r + r2 = 7

Solving for variable 'r'.

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

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

Factor a trinomial.
(-1 + -1r)(7 + -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 '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {-1, 7}