9x^3+6x^2+12x=0

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Solution for 9x^3+6x^2+12x=0 equation:


Simplifying
9x3 + 6x2 + 12x = 0

Reorder the terms:
12x + 6x2 + 9x3 = 0

Solving
12x + 6x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(4 + 2x + 3x2) = 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 '(4 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 2x + 3x2 = 0 Solving 4 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.6666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + -1.333333333 0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.6666666667x + x2 = -1.333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + 0.6666666667x + x2 = -1.2222222218 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -1.2222222218 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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