r^2-6r=20+2r

Solution for r^2-6r=20+2r equation:

Simplifying
r2 + -6r = 20 + 2r

Reorder the terms:
-6r + r2 = 20 + 2r

Solving
-6r + r2 = 20 + 2r

Solving for variable 'r'.

Reorder the terms:
-20 + -6r + -2r + r2 = 20 + 2r + -20 + -2r

Combine like terms: -6r + -2r = -8r
-20 + -8r + r2 = 20 + 2r + -20 + -2r

Reorder the terms:
-20 + -8r + r2 = 20 + -20 + 2r + -2r

Combine like terms: 20 + -20 = 0
-20 + -8r + r2 = 0 + 2r + -2r
-20 + -8r + r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-20 + -8r + r2 = 0

Factor a trinomial.
(-2 + -1r)(10 + -1r) = 0

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-2, 10}