r^2=-5+6r

Solution for r^2=-5+6r equation:

Simplifying
r2 = -5 + 6r

Solving
r2 = -5 + 6r

Solving for variable 'r'.

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

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

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

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

Factor a trinomial.
(1 + -1r)(5 + -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 '(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
Solution
r = {1, 5}