12x^9-47x^5+45x=0

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Solution for 12x^9-47x^5+45x=0 equation:


Simplifying
12x9 + -47x5 + 45x = 0

Reorder the terms:
45x + -47x5 + 12x9 = 0

Solving
45x + -47x5 + 12x9 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(45 + -47x4 + 12x8) = 0

Factor a trinomial.
x((5 + -3x4)(9 + -4x4)) = 0

Factor a difference between two squares.
x((5 + -3x4)((3 + 2x2)(3 + -2x2))) = 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 '(5 + -3x4)' equal to zero and attempt to solve: Simplifying 5 + -3x4 = 0 Solving 5 + -3x4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x4 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x4 = 0 + -5 -3x4 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x4 = -5 Divide each side by '-3'. x4 = 1.666666667 Simplifying x4 = 1.666666667 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(3 + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 2x2 = 0 Solving 3 + 2x2 = 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 + 2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x2 = 0 + -3 2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x2 = -3 Divide each side by '2'. x2 = -1.5 Simplifying x2 = -1.5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 4

Set the factor '(3 + -2x2)' equal to zero and attempt to solve: Simplifying 3 + -2x2 = 0 Solving 3 + -2x2 = 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 + -2x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x2 = 0 + -3 -2x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -2x2 = -3 Divide each side by '-2'. x2 = 1.5 Simplifying x2 = 1.5 Take the square root of each side: x = {-1.224744871, 1.224744871}

Solution

x = {0, -1.224744871, 1.224744871}

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