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

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


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

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

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

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

Combine like terms: -25x2 + -16x2 = -41x2
(400 + -41x2 + x4) = 0

Solving
400 + -41x2 + x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((4 + x)(4 + -1x))(25 + -1x2) = 0

Factor a difference between two squares.
((5 + x)(5 + -1x))(4 + x)(4 + -1x) = 0


Subproblem 1
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 2
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

Subproblem 3
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 4
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 = {-4, 4, -5, 5}

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