2x-10x^2+16x^3-8x^2+20x^3=0

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Solution for 2x-10x^2+16x^3-8x^2+20x^3=0 equation:


Simplifying
2x + -10x2 + 16x3 + -8x2 + 20x3 = 0

Reorder the terms:
2x + -10x2 + -8x2 + 16x3 + 20x3 = 0

Combine like terms: -10x2 + -8x2 = -18x2
2x + -18x2 + 16x3 + 20x3 = 0

Combine like terms: 16x3 + 20x3 = 36x3
2x + -18x2 + 36x3 = 0

Solving
2x + -18x2 + 36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -9x + 18x2) = 0

Factor a trinomial.
2x((1 + -6x)(1 + -3x)) = 0

Ignore the factor 2.

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 '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Divide each side by '-6'. x = 0.1666666667 Simplifying x = 0.1666666667

Subproblem 3

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {0, 0.1666666667, 0.3333333333}

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