12x^3+17x^2+42x=0

Solution for 12x^3+17x^2+42x=0 equation:

Simplifying
12x3 + 17x2 + 42x = 0

Reorder the terms:
42x + 17x2 + 12x3 = 0

Solving
42x + 17x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(42 + 17x + 12x2) = 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 '(42 + 17x + 12x2)' equal to zero and attempt to solve:

Simplifying
42 + 17x + 12x2 = 0

Solving
42 + 17x + 12x2 = 0

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

Divide each side by '12'.
3.5 + 1.416666667x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 1.416666667x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 1.416666667x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 1.416666667x + x2 = 0 + -3.5
1.416666667x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
1.416666667x + x2 = -3.5

The x term is 1.416666667x.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667x + 0.5017361113 + x2 = -3.5 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667x + x2 = -3.5 + 0.5017361113

Combine like terms: -3.5 + 0.5017361113 = -2.9982638887
0.5017361113 + 1.416666667x + x2 = -2.9982638887

Factor a perfect square on the left side:
(x + 0.7083333335)(x + 0.7083333335) = -2.9982638887

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}