r^2+5r+3r=9

Solution for r^2+5r+3r=9 equation:

Simplifying
r2 + 5r + 3r = 9

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

Combine like terms: 5r + 3r = 8r
8r + r2 = 9

Solving
8r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-9 + 8r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 8r + r2 = 0

Factor a trinomial.
(-9 + -1r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-9 + -1r)' equal to zero and attempt to solve:

Simplifying
-9 + -1r = 0

Solving
-9 + -1r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 0 + 9
-1r = 0 + 9

Combine like terms: 0 + 9 = 9
-1r = 9

Divide each side by '-1'.
r = -9

Simplifying
r = -9
Subproblem 2
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
Solution
r = {-9, 1}