r^2=6-r

Solution for r^2=6-r equation:

Simplifying
r2 = 6 + -1r

Solving
r2 = 6 + -1r

Solving for variable 'r'.

Reorder the terms:
-6 + r + r2 = 6 + -1r + -6 + r

Reorder the terms:
-6 + r + r2 = 6 + -6 + -1r + r

Combine like terms: 6 + -6 = 0
-6 + r + r2 = 0 + -1r + r
-6 + r + r2 = -1r + r

Combine like terms: -1r + r = 0
-6 + r + r2 = 0

Factor a trinomial.
(-3 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
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
Solution
r = {-3, 2}