9(r^2+2r)=6r^2

Solution for 9(r^2+2r)=6r^2 equation:

Simplifying
9(r2 + 2r) = 6r2

Reorder the terms:
9(2r + r2) = 6r2
(2r * 9 + r2 * 9) = 6r2
(18r + 9r2) = 6r2

Solving
18r + 9r2 = 6r2

Solving for variable 'r'.

Combine like terms: 9r2 + -6r2 = 3r2
18r + 3r2 = 6r2 + -6r2

Combine like terms: 6r2 + -6r2 = 0
18r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3r'.
3r(6 + r) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

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

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

Simplifying
r = -6
Solution
r = {0, -6}