6x=11x^2-3x^3

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Solution for 6x=11x^2-3x^3 equation:


Simplifying
6x = 11x2 + -3x3

Solving
6x = 11x2 + -3x3

Solving for variable 'x'.

Reorder the terms:
6x + -11x2 + 3x3 = 11x2 + -11x2 + -3x3 + 3x3

Combine like terms: 11x2 + -11x2 = 0
6x + -11x2 + 3x3 = 0 + -3x3 + 3x3
6x + -11x2 + 3x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
6x + -11x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -11x + 3x2) = 0

Factor a trinomial.
x((2 + -3x)(3 + -1x)) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Subproblem 3

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, 0.6666666667, 3}

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