(x^2-9)(x^2-16)=0

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Solution for (x^2-9)(x^2-16)=0 equation: 


Simplifying
(x2 + -9)(x2 + -16) = 0

Reorder the terms:
(-9 + x2)(x2 + -16) = 0

Reorder the terms:
(-9 + x2)(-16 + x2) = 0

Multiply (-9 + x2) * (-16 + x2)
(-9(-16 + x2) + x2(-16 + x2)) = 0
((-16 * -9 + x2 * -9) + x2(-16 + x2)) = 0
((144 + -9x2) + x2(-16 + x2)) = 0
(144 + -9x2 + (-16 * x2 + x2 * x2)) = 0
(144 + -9x2 + (-16x2 + x4)) = 0

Combine like terms: -9x2 + -16x2 = -25x2
(144 + -25x2 + x4) = 0

Solving
144 + -25x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(16 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(16 + -1x2) = 0

Factor a difference between two squares.
((4 + x)(4 + -1x))(3 + x)(3 + -1x) = 0


Subproblem 1
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 2
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

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 = {-3, 3, -4, 4}

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