18x^3+24x^2-12x=0

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Solution for 18x^3+24x^2-12x=0 equation:


Simplifying
18x3 + 24x2 + -12x = 0

Reorder the terms:
-12x + 24x2 + 18x3 = 0

Solving
-12x + 24x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-2 + 4x + 3x2) = 0

Ignore the factor 6.

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 '(-2 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + 3x2 = 0 Solving -2 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 1.333333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 1.333333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.6666666667 1.333333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 1.333333333x + x2 = 0.6666666667 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.6666666667 + 0.4444444442 Combine like terms: 0.6666666667 + 0.4444444442 = 1.1111111109 0.4444444442 + 1.333333333x + x2 = 1.1111111109 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.1111111109 Calculate the square root of the right side: 1.054092553 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.054092553 and -1.054092553.

Subproblem 1

x + 0.6666666665 = 1.054092553 Simplifying x + 0.6666666665 = 1.054092553 Reorder the terms: 0.6666666665 + x = 1.054092553 Solving 0.6666666665 + x = 1.054092553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.054092553 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.054092553 + -0.6666666665 x = 1.054092553 + -0.6666666665 Combine like terms: 1.054092553 + -0.6666666665 = 0.3874258865 x = 0.3874258865 Simplifying x = 0.3874258865

Subproblem 2

x + 0.6666666665 = -1.054092553 Simplifying x + 0.6666666665 = -1.054092553 Reorder the terms: 0.6666666665 + x = -1.054092553 Solving 0.6666666665 + x = -1.054092553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.054092553 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.054092553 + -0.6666666665 x = -1.054092553 + -0.6666666665 Combine like terms: -1.054092553 + -0.6666666665 = -1.7207592195 x = -1.7207592195 Simplifying x = -1.7207592195

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3874258865, -1.7207592195}

Solution

x = {0, 0.3874258865, -1.7207592195}

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