12x^3+32x^2+84x=0

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Solution for 12x^3+32x^2+84x=0 equation:


Simplifying
12x3 + 32x2 + 84x = 0

Reorder the terms:
84x + 32x2 + 12x3 = 0

Solving
84x + 32x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(21 + 8x + 3x2) = 0

Ignore the factor 4.

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 '(21 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 21 + 8x + 3x2 = 0 Solving 21 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 2.666666667x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 2.666666667x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2.666666667x + x2 = 0 + -7 2.666666667x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 2.666666667x + x2 = -7 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -7 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -7 + 1.777777780 Combine like terms: -7 + 1.777777780 = -5.22222222 1.777777780 + 2.666666667x + x2 = -5.22222222 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -5.22222222 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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