(6x^3+9x^2+12x)=

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


Simplifying
(6x3 + 9x2 + 12x) = 0

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

Remove parenthesis around (12x + 9x2 + 6x3)
12x + 9x2 + 6x3 = 0

Solving
12x + 9x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(4 + 3x + 2x2) = 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 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 2x2 = 0 Solving 4 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.5x + x2 = 0 + -2 1.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.5x + x2 = -2 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2 + 0.5625 Combine like terms: -2 + 0.5625 = -1.4375 0.5625 + 1.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.4375 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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