6x^3+17x^2+72x=

Solution for 6x^3+17x^2+72x= equation:

Simplifying
6x3 + 17x2 + 72x = 0

Reorder the terms:
72x + 17x2 + 6x3 = 0

Solving
72x + 17x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(72 + 17x + 6x2) = 0

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 '(72 + 17x + 6x2)' equal to zero and attempt to solve:

Simplifying
72 + 17x + 6x2 = 0

Solving
72 + 17x + 6x2 = 0

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

Divide each side by '6'.
12 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 2.833333333x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 2.833333333x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 2.833333333x + x2 = 0 + -12
2.833333333x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
2.833333333x + x2 = -12

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = -12 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = -12 + 2.006944445

Combine like terms: -12 + 2.006944445 = -9.993055555
2.006944445 + 2.833333333x + x2 = -9.993055555

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = -9.993055555

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}