0=(x^2+16)(x^2-25)

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Solution for 0=(x^2+16)(x^2-25) equation: 


Simplifying
0 = (x2 + 16)(x2 + -25)

Reorder the terms:
0 = (16 + x2)(x2 + -25)

Reorder the terms:
0 = (16 + x2)(-25 + x2)

Multiply (16 + x2) * (-25 + x2)
0 = (16(-25 + x2) + x2(-25 + x2))
0 = ((-25 * 16 + x2 * 16) + x2(-25 + x2))
0 = ((-400 + 16x2) + x2(-25 + x2))
0 = (-400 + 16x2 + (-25 * x2 + x2 * x2))
0 = (-400 + 16x2 + (-25x2 + x4))

Combine like terms: 16x2 + -25x2 = -9x2
0 = (-400 + -9x2 + x4)

Solving
0 = -400 + -9x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 400 = 400
400 + 9x2 + -1x4 = -400 + -9x2 + x4 + 400 + 9x2 + -1x4

Reorder the terms:
400 + 9x2 + -1x4 = -400 + 400 + -9x2 + 9x2 + x4 + -1x4

Combine like terms: -400 + 400 = 0
400 + 9x2 + -1x4 = 0 + -9x2 + 9x2 + x4 + -1x4
400 + 9x2 + -1x4 = -9x2 + 9x2 + x4 + -1x4

Combine like terms: -9x2 + 9x2 = 0
400 + 9x2 + -1x4 = 0 + x4 + -1x4
400 + 9x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
400 + 9x2 + -1x4 = 0

Factor a trinomial.
(25 + -1x2)(16 + x2) = 0

Factor a difference between two squares.
((5 + x)(5 + -1x))(16 + x2) = 0


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

Simplifying
16 + x2 = 0

Solving
16 + x2 = 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 + x2 = 0 + -16

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

Combine like terms: 0 + -16 = -16
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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-5, 5}

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