(x-5)(x+5)(x^2-25)=

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Solution for (x-5)(x+5)(x^2-25)= equation: 


Simplifying
(x + -5)(x + 5)(x2 + -25) = 0

Reorder the terms:
(-5 + x)(x + 5)(x2 + -25) = 0

Reorder the terms:
(-5 + x)(5 + x)(x2 + -25) = 0

Reorder the terms:
(-5 + x)(5 + x)(-25 + x2) = 0

Multiply (-5 + x) * (5 + x)
(-5(5 + x) + x(5 + x))(-25 + x2) = 0
((5 * -5 + x * -5) + x(5 + x))(-25 + x2) = 0
((-25 + -5x) + x(5 + x))(-25 + x2) = 0
(-25 + -5x + (5 * x + x * x))(-25 + x2) = 0
(-25 + -5x + (5x + x2))(-25 + x2) = 0

Combine like terms: -5x + 5x = 0
(-25 + 0 + x2)(-25 + x2) = 0
(-25 + x2)(-25 + x2) = 0

Multiply (-25 + x2) * (-25 + x2)
(-25(-25 + x2) + x2(-25 + x2)) = 0
((-25 * -25 + x2 * -25) + x2(-25 + x2)) = 0
((625 + -25x2) + x2(-25 + x2)) = 0
(625 + -25x2 + (-25 * x2 + x2 * x2)) = 0
(625 + -25x2 + (-25x2 + x4)) = 0

Combine like terms: -25x2 + -25x2 = -50x2
(625 + -50x2 + x4) = 0

Solving
625 + -50x2 + x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
((5 + x)(5 + -1x))(25 + -1x2) = 0

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


Subproblem 1
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 2
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

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 = {-5, 5, -5, 5}

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