6r^3+5r^2+2r=9r^2+4r

Solution for 6r^3+5r^2+2r=9r^2+4r equation:

Simplifying
6r3 + 5r2 + 2r = 9r2 + 4r

Reorder the terms:
2r + 5r2 + 6r3 = 9r2 + 4r

Reorder the terms:
2r + 5r2 + 6r3 = 4r + 9r2

Solving
2r + 5r2 + 6r3 = 4r + 9r2

Solving for variable 'r'.

Reorder the terms:
2r + -4r + 5r2 + -9r2 + 6r3 = 4r + 9r2 + -4r + -9r2

Combine like terms: 2r + -4r = -2r
-2r + 5r2 + -9r2 + 6r3 = 4r + 9r2 + -4r + -9r2

Combine like terms: 5r2 + -9r2 = -4r2
-2r + -4r2 + 6r3 = 4r + 9r2 + -4r + -9r2

Reorder the terms:
-2r + -4r2 + 6r3 = 4r + -4r + 9r2 + -9r2

Combine like terms: 4r + -4r = 0
-2r + -4r2 + 6r3 = 0 + 9r2 + -9r2
-2r + -4r2 + 6r3 = 9r2 + -9r2

Combine like terms: 9r2 + -9r2 = 0
-2r + -4r2 + 6r3 = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-1 + -2r + 3r2) = 0

Factor a trinomial.
2r((-1 + -3r)(1 + -1r)) = 0

Ignore the factor 2.
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 '(-1 + -3r)' equal to zero and attempt to solve:

Simplifying
-1 + -3r = 0

Solving
-1 + -3r = 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 + -3r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3r = 0 + 1
-3r = 0 + 1

Combine like terms: 0 + 1 = 1
-3r = 1

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 3
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 = {0, -0.3333333333, 1}