(3x^3-40x^2-16x)=

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Solution for (3x^3-40x^2-16x)= equation:


Simplifying
(3x3 + -40x2 + -16x) = 0

Reorder the terms:
(-16x + -40x2 + 3x3) = 0

Remove parenthesis around (-16x + -40x2 + 3x3)
-16x + -40x2 + 3x3 = 0

Solving
-16x + -40x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-16 + -40x + 3x2) = 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 '(-16 + -40x + 3x2)' equal to zero and attempt to solve: Simplifying -16 + -40x + 3x2 = 0 Solving -16 + -40x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -13.33333333x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -13.33333333x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -13.33333333x + x2 = 0 + 5.333333333 -13.33333333x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -13.33333333x + x2 = 5.333333333 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = 5.333333333 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = 5.333333333 + 44.44444442 Combine like terms: 5.333333333 + 44.44444442 = 49.777777753 44.44444442 + -13.33333333x + x2 = 49.777777753 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 49.777777753 Calculate the square root of the right side: 7.055336828 Break this problem into two subproblems by setting (x + -6.666666665) equal to 7.055336828 and -7.055336828.

Subproblem 1

x + -6.666666665 = 7.055336828 Simplifying x + -6.666666665 = 7.055336828 Reorder the terms: -6.666666665 + x = 7.055336828 Solving -6.666666665 + x = 7.055336828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 7.055336828 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 7.055336828 + 6.666666665 x = 7.055336828 + 6.666666665 Combine like terms: 7.055336828 + 6.666666665 = 13.722003493 x = 13.722003493 Simplifying x = 13.722003493

Subproblem 2

x + -6.666666665 = -7.055336828 Simplifying x + -6.666666665 = -7.055336828 Reorder the terms: -6.666666665 + x = -7.055336828 Solving -6.666666665 + x = -7.055336828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -7.055336828 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -7.055336828 + 6.666666665 x = -7.055336828 + 6.666666665 Combine like terms: -7.055336828 + 6.666666665 = -0.388670163 x = -0.388670163 Simplifying x = -0.388670163

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.722003493, -0.388670163}

Solution

x = {0, 13.722003493, -0.388670163}

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