(x^2-9)(x^2-25)=0

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Solution for (x^2-9)(x^2-25)=0 equation: 


Simplifying
(x2 + -9)(x2 + -25) = 0

Reorder the terms:
(-9 + x2)(x2 + -25) = 0

Reorder the terms:
(-9 + x2)(-25 + x2) = 0

Multiply (-9 + x2) * (-25 + x2)
(-9(-25 + x2) + x2(-25 + x2)) = 0
((-25 * -9 + x2 * -9) + x2(-25 + x2)) = 0
((225 + -9x2) + x2(-25 + x2)) = 0
(225 + -9x2 + (-25 * x2 + x2 * x2)) = 0
(225 + -9x2 + (-25x2 + x4)) = 0

Combine like terms: -9x2 + -25x2 = -34x2
(225 + -34x2 + x4) = 0

Solving
225 + -34x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(25 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(25 + -1x2) = 0

Factor a difference between two squares.
((5 + x)(5 + -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 '(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 = {-3, 3, -5, 5}

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