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

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Solution for (8-x^2)(x-x^3)=0 equation: 


Simplifying
(8 + -1x2)(x + -1x3) = 0

Multiply (8 + -1x2) * (x + -1x3)
(8(x + -1x3) + -1x2 * (x + -1x3)) = 0
((x * 8 + -1x3 * 8) + -1x2 * (x + -1x3)) = 0
((8x + -8x3) + -1x2 * (x + -1x3)) = 0
(8x + -8x3 + (x * -1x2 + -1x3 * -1x2)) = 0
(8x + -8x3 + (-1x3 + 1x5)) = 0

Combine like terms: -8x3 + -1x3 = -9x3
(8x + -9x3 + 1x5) = 0

Solving
8x + -9x3 + 1x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + -9x2 + x4) = 0

Factor a trinomial.
x((1 + -1x2)(8 + -1x2)) = 0

Factor a difference between two squares.
x(((1 + x)(1 + -1x))(8 + -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 '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}

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, -2.828427125, 2.828427125, -1, 1}

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