3r^2+8r^2=9r+5r^2

Solution for 3r^2+8r^2=9r+5r^2 equation:

Simplifying
3r2 + 8r2 = 9r + 5r2

Combine like terms: 3r2 + 8r2 = 11r2
11r2 = 9r + 5r2

Solving
11r2 = 9r + 5r2

Solving for variable 'r'.

Reorder the terms:
-9r + 11r2 + -5r2 = 9r + 5r2 + -9r + -5r2

Combine like terms: 11r2 + -5r2 = 6r2
-9r + 6r2 = 9r + 5r2 + -9r + -5r2

Reorder the terms:
-9r + 6r2 = 9r + -9r + 5r2 + -5r2

Combine like terms: 9r + -9r = 0
-9r + 6r2 = 0 + 5r2 + -5r2
-9r + 6r2 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
-9r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '3r'.
3r(-3 + 2r) = 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 '(-3 + 2r)' equal to zero and attempt to solve:

Simplifying
-3 + 2r = 0

Solving
-3 + 2r = 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 + 2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2r = 0 + 3
2r = 0 + 3

Combine like terms: 0 + 3 = 3
2r = 3

Divide each side by '2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {0, 1.5}