((x^2)+16)((x^2)-49)=0

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Solution for ((x^2)+16)((x^2)-49)=0 equation: 


Simplifying
((x2) + 16)((x2) + -49) = 0
(x2 + 16)((x2) + -49) = 0

Reorder the terms:
(16 + x2)((x2) + -49) = 0
(16 + x2)(x2 + -49) = 0

Reorder the terms:
(16 + x2)(-49 + x2) = 0

Multiply (16 + x2) * (-49 + x2)
(16(-49 + x2) + x2(-49 + x2)) = 0
((-49 * 16 + x2 * 16) + x2(-49 + x2)) = 0
((-784 + 16x2) + x2(-49 + x2)) = 0
(-784 + 16x2 + (-49 * x2 + x2 * x2)) = 0
(-784 + 16x2 + (-49x2 + x4)) = 0

Combine like terms: 16x2 + -49x2 = -33x2
(-784 + -33x2 + x4) = 0

Solving
-784 + -33x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-16 + -1x2)(49 + -1x2) = 0

Factor a difference between two squares.
(-16 + -1x2)((7 + x)(7 + -1x)) = 0


Subproblem 1
Set the factor '(-16 + -1x2)' equal to zero and attempt to solve:

Simplifying
-16 + -1x2 = 0

Solving
-16 + -1x2 = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x2 = 0 + 16
-1x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1x2 = 16

Divide each side by '-1'.
x2 = -16

Simplifying
x2 = -16

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-7, 7}

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