21x^3-9x^2+24x=

Solution for 21x^3-9x^2+24x= equation:

Simplifying
21x3 + -9x2 + 24x = 0

Reorder the terms:
24x + -9x2 + 21x3 = 0

Solving
24x + -9x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(8 + -3x + 7x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(8 + -3x + 7x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x + 7x2 = 0

Solving
8 + -3x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
1.142857143 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + -0.4285714286x + -1.142857143 + x2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + -0.4285714286x + x2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + -0.4285714286x + x2 = 0 + -1.142857143
-0.4285714286x + x2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
-0.4285714286x + x2 = -1.142857143

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = -1.142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = -1.142857143 + 0.04591836735

Combine like terms: -1.142857143 + 0.04591836735 = -1.09693877565
0.04591836735 + -0.4285714286x + x2 = -1.09693877565

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = -1.09693877565

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}