6x^4+6x^2=20x^3

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Solution for 6x^4+6x^2=20x^3 equation:


Simplifying
6x4 + 6x2 = 20x3

Reorder the terms:
6x2 + 6x4 = 20x3

Solving
6x2 + 6x4 = 20x3

Solving for variable 'x'.

Reorder the terms:
6x2 + -20x3 + 6x4 = 20x3 + -20x3

Combine like terms: 20x3 + -20x3 = 0
6x2 + -20x3 + 6x4 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(3 + -10x + 3x2) = 0

Factor a trinomial.
2x2((1 + -3x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

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

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, 0.3333333333, 3}

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