r^2-8r=-3r+6

Solution for r^2-8r=-3r+6 equation:

Simplifying
r2 + -8r = -3r + 6

Reorder the terms:
-8r + r2 = -3r + 6

Reorder the terms:
-8r + r2 = 6 + -3r

Solving
-8r + r2 = 6 + -3r

Solving for variable 'r'.

Reorder the terms:
-6 + -8r + 3r + r2 = 6 + -3r + -6 + 3r

Combine like terms: -8r + 3r = -5r
-6 + -5r + r2 = 6 + -3r + -6 + 3r

Reorder the terms:
-6 + -5r + r2 = 6 + -6 + -3r + 3r

Combine like terms: 6 + -6 = 0
-6 + -5r + r2 = 0 + -3r + 3r
-6 + -5r + r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
-6 + -5r + 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}