0=x(-x^2+4)

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Solution for 0=x(-x^2+4) equation:


Simplifying
0 = x(-1x2 + 4)

Reorder the terms:
0 = x(4 + -1x2)
0 = (4 * x + -1x2 * x)
0 = (4x + -1x3)

Solving
0 = 4x + -1x3

Solving for variable 'x'.
Remove the zero:
-4x + x3 = 4x + -1x3 + -4x + x3

Reorder the terms:
-4x + x3 = 4x + -4x + -1x3 + x3

Combine like terms: 4x + -4x = 0
-4x + x3 = 0 + -1x3 + x3
-4x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-4x + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x2) = 0

Factor a difference between two squares.
x((2 + x)(-2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 3

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Solution

x = {0, -2, 2}

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