(x^2-4)(x^2-16)=0

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Solution for (x^2-4)(x^2-16)=0 equation:


Simplifying
(x2 + -4)(x2 + -16) = 0

Reorder the terms:
(-4 + x2)(x2 + -16) = 0

Reorder the terms:
(-4 + x2)(-16 + x2) = 0

Multiply (-4 + x2) * (-16 + x2)
(-4(-16 + x2) + x2(-16 + x2)) = 0
((-16 * -4 + x2 * -4) + x2(-16 + x2)) = 0
((64 + -4x2) + x2(-16 + x2)) = 0
(64 + -4x2 + (-16 * x2 + x2 * x2)) = 0
(64 + -4x2 + (-16x2 + x4)) = 0

Combine like terms: -4x2 + -16x2 = -20x2
(64 + -20x2 + x4) = 0

Solving
64 + -20x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(2 + x)(2 + -1x) = 0

Subproblem 1

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 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 3

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 4

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-2, 2, -4, 4}

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