12x^3+23x^2+9x=0

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Solution for 12x^3+23x^2+9x=0 equation:


Simplifying
12x3 + 23x2 + 9x = 0

Reorder the terms:
9x + 23x2 + 12x3 = 0

Solving
9x + 23x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 23x + 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 '(9 + 23x + 12x2)' equal to zero and attempt to solve: Simplifying 9 + 23x + 12x2 = 0 Solving 9 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.75 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.916666667x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.916666667x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.916666667x + x2 = 0 + -0.75 1.916666667x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.916666667x + x2 = -0.75 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = -0.75 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = -0.75 + 0.9184027781 Combine like terms: -0.75 + 0.9184027781 = 0.1684027781 0.9184027781 + 1.916666667x + x2 = 0.1684027781 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = 0.1684027781 Calculate the square root of the right side: 0.410369075 Break this problem into two subproblems by setting (x + 0.9583333335) equal to 0.410369075 and -0.410369075.

Subproblem 1

x + 0.9583333335 = 0.410369075 Simplifying x + 0.9583333335 = 0.410369075 Reorder the terms: 0.9583333335 + x = 0.410369075 Solving 0.9583333335 + x = 0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = 0.410369075 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 0.410369075 + -0.9583333335 x = 0.410369075 + -0.9583333335 Combine like terms: 0.410369075 + -0.9583333335 = -0.5479642585 x = -0.5479642585 Simplifying x = -0.5479642585

Subproblem 2

x + 0.9583333335 = -0.410369075 Simplifying x + 0.9583333335 = -0.410369075 Reorder the terms: 0.9583333335 + x = -0.410369075 Solving 0.9583333335 + x = -0.410369075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = -0.410369075 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -0.410369075 + -0.9583333335 x = -0.410369075 + -0.9583333335 Combine like terms: -0.410369075 + -0.9583333335 = -1.3687024085 x = -1.3687024085 Simplifying x = -1.3687024085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.5479642585, -1.3687024085}

Solution

x = {0, -0.5479642585, -1.3687024085}

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