14r^4-33r^3+18r^2=0

Solution for 14r^4-33r^3+18r^2=0 equation:

Simplifying
14r4 + -33r3 + 18r2 = 0

Reorder the terms:
18r2 + -33r3 + 14r4 = 0

Solving
18r2 + -33r3 + 14r4 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r2'.
r2(18 + -33r + 14r2) = 0

Factor a trinomial.
r2((6 + -7r)(3 + -2r)) = 0

Subproblem 1
Set the factor 'r2' equal to zero and attempt to solve:

Simplifying
r2 = 0

Solving
r2 = 0

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

Simplifying
r2 = 0

Take the square root of each side:
r = {0}
Subproblem 2
Set the factor '(6 + -7r)' equal to zero and attempt to solve:

Simplifying
6 + -7r = 0

Solving
6 + -7r = 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 + -7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7r = 0 + -6
-7r = 0 + -6

Combine like terms: 0 + -6 = -6
-7r = -6

Divide each side by '-7'.
r = 0.8571428571

Simplifying
r = 0.8571428571
Subproblem 3
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, 0.8571428571, 1.5}