5x^3+11x^2+12x=0

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Solution for 5x^3+11x^2+12x=0 equation: 


Simplifying
5x3 + 11x2 + 12x = 0

Reorder the terms:
12x + 11x2 + 5x3 = 0

Solving
12x + 11x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(12 + 11x + 5x2) = 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 '(12 + 11x + 5x2)' equal to zero and attempt to solve:

Simplifying
12 + 11x + 5x2 = 0

Solving
12 + 11x + 5x2 = 0

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

Divide each side by '5'.
2.4 + 2.2x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 2.2x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 2.2x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 2.2x + x2 = 0 + -2.4
2.2x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
2.2x + x2 = -2.4

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = -2.4 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = -2.4 + 1.21

Combine like terms: -2.4 + 1.21 = -1.19
1.21 + 2.2x + x2 = -1.19

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = -1.19

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}

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