9+(r-5)r=3

Solution for 9+(r-5)r=3 equation:

Simplifying
9 + (r + -5) * r = 3

Reorder the terms:
9 + (-5 + r) * r = 3

Reorder the terms for easier multiplication:
9 + r(-5 + r) = 3
9 + (-5 * r + r * r) = 3
9 + (-5r + r2) = 3

Solving
9 + -5r + r2 = 3

Solving for variable 'r'.

Reorder the terms:
9 + -3 + -5r + r2 = 3 + -3

Combine like terms: 9 + -3 = 6
6 + -5r + r2 = 3 + -3

Combine like terms: 3 + -3 = 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}