x^2(x^3-10x)=-9x

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Solution for x^2(x^3-10x)=-9x equation:


Simplifying
x2(x3 + -10x) = -9x

Reorder the terms:
x2(-10x + x3) = -9x
(-10x * x2 + x3 * x2) = -9x
(-10x3 + x5) = -9x

Solving
-10x3 + x5 = -9x

Solving for variable 'x'.

Reorder the terms:
9x + -10x3 + x5 = -9x + 9x

Combine like terms: -9x + 9x = 0
9x + -10x3 + x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -10x2 + x4) = 0

Factor a trinomial.
x((1 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
x(((1 + x)(1 + -1x))(9 + -1x2)) = 0

Factor a difference between two squares.
x(((3 + x)(3 + -1x))(1 + x)(1 + -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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 3

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Subproblem 4

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 5

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, -1, 1, -3, 3}

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