r^2-5r+13=7

Solution for r^2-5r+13=7 equation:

Simplifying
r2 + -5r + 13 = 7

Reorder the terms:
13 + -5r + r2 = 7

Solving
13 + -5r + r2 = 7

Solving for variable 'r'.

Reorder the terms:
13 + -7 + -5r + r2 = 7 + -7

Combine like terms: 13 + -7 = 6
6 + -5r + r2 = 7 + -7

Combine like terms: 7 + -7 = 0
6 + -5r + r2 = 0

Factor a trinomial.
(2 + -1r)(3 + -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 '(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
Solution
r = {2, 3}