(x^3-25x)(9-x^2)=0

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Solution for (x^3-25x)(9-x^2)=0 equation:


Simplifying
(x3 + -25x)(9 + -1x2) = 0

Reorder the terms:
(-25x + x3)(9 + -1x2) = 0

Multiply (-25x + x3) * (9 + -1x2)
(-25x * (9 + -1x2) + x3(9 + -1x2)) = 0
((9 * -25x + -1x2 * -25x) + x3(9 + -1x2)) = 0
((-225x + 25x3) + x3(9 + -1x2)) = 0
(-225x + 25x3 + (9 * x3 + -1x2 * x3)) = 0
(-225x + 25x3 + (9x3 + -1x5)) = 0

Combine like terms: 25x3 + 9x3 = 34x3
(-225x + 34x3 + -1x5) = 0

Solving
-225x + 34x3 + -1x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-225 + 34x2 + -1x4) = 0

Factor a trinomial.
x((-25 + x2)(9 + -1x2)) = 0

Factor a difference between two squares.
x(((5 + x)(-5 + x))(9 + -1x2)) = 0

Factor a difference between two squares.
x(((3 + x)(3 + -1x))(5 + x)(-5 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Subproblem 3

Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5

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, -5, 5, -3, 3}

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