(5-x^2)(x-x^3)=0

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Solution for (5-x^2)(x-x^3)=0 equation: 


Simplifying
(5 + -1x2)(x + -1x3) = 0

Multiply (5 + -1x2) * (x + -1x3)
(5(x + -1x3) + -1x2 * (x + -1x3)) = 0
((x * 5 + -1x3 * 5) + -1x2 * (x + -1x3)) = 0
((5x + -5x3) + -1x2 * (x + -1x3)) = 0
(5x + -5x3 + (x * -1x2 + -1x3 * -1x2)) = 0
(5x + -5x3 + (-1x3 + 1x5)) = 0

Combine like terms: -5x3 + -1x3 = -6x3
(5x + -6x3 + 1x5) = 0

Solving
5x + -6x3 + 1x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -6x2 + x4) = 0

Factor a trinomial.
x((1 + -1x2)(5 + -1x2)) = 0

Factor a difference between two squares.
x(((1 + x)(1 + -1x))(5 + -1x2)) = 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 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 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 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

Subproblem 3
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 4
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
Solution
x = {0, -2.236067978, 2.236067978, -1, 1}

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