(x+2)(x-2)(x+5)(x-5)=0

Solution for (x+2)(x-2)(x+5)(x-5)=0 equation:

Simplifying
(x + 2)(x + -2)(x + 5)(x + -5) = 0

Reorder the terms:
(2 + x)(x + -2)(x + 5)(x + -5) = 0

Reorder the terms:
(2 + x)(-2 + x)(x + 5)(x + -5) = 0

Reorder the terms:
(2 + x)(-2 + x)(5 + x)(x + -5) = 0

Reorder the terms:
(2 + x)(-2 + x)(5 + x)(-5 + x) = 0

Multiply (2 + x) * (-2 + x)
(2(-2 + x) + x(-2 + x))(5 + x)(-5 + x) = 0
((-2 * 2 + x * 2) + x(-2 + x))(5 + x)(-5 + x) = 0
((-4 + 2x) + x(-2 + x))(5 + x)(-5 + x) = 0
(-4 + 2x + (-2 * x + x * x))(5 + x)(-5 + x) = 0
(-4 + 2x + (-2x + x2))(5 + x)(-5 + x) = 0

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2)(5 + x)(-5 + x) = 0
(-4 + x2)(5 + x)(-5 + x) = 0

Multiply (-4 + x2) * (5 + x)
(-4(5 + x) + x2(5 + x))(-5 + x) = 0
((5 * -4 + x * -4) + x2(5 + x))(-5 + x) = 0
((-20 + -4x) + x2(5 + x))(-5 + x) = 0
(-20 + -4x + (5 * x2 + x * x2))(-5 + x) = 0
(-20 + -4x + (5x2 + x3))(-5 + x) = 0
(-20 + -4x + 5x2 + x3)(-5 + x) = 0

Multiply (-20 + -4x + 5x2 + x3) * (-5 + x)
(-20(-5 + x) + -4x * (-5 + x) + 5x2 * (-5 + x) + x3(-5 + x)) = 0
((-5 * -20 + x * -20) + -4x * (-5 + x) + 5x2 * (-5 + x) + x3(-5 + x)) = 0
((100 + -20x) + -4x * (-5 + x) + 5x2 * (-5 + x) + x3(-5 + x)) = 0
(100 + -20x + (-5 * -4x + x * -4x) + 5x2 * (-5 + x) + x3(-5 + x)) = 0
(100 + -20x + (20x + -4x2) + 5x2 * (-5 + x) + x3(-5 + x)) = 0
(100 + -20x + 20x + -4x2 + (-5 * 5x2 + x * 5x2) + x3(-5 + x)) = 0
(100 + -20x + 20x + -4x2 + (-25x2 + 5x3) + x3(-5 + x)) = 0
(100 + -20x + 20x + -4x2 + -25x2 + 5x3 + (-5 * x3 + x * x3)) = 0
(100 + -20x + 20x + -4x2 + -25x2 + 5x3 + (-5x3 + x4)) = 0

Combine like terms: -20x + 20x = 0
(100 + 0 + -4x2 + -25x2 + 5x3 + -5x3 + x4) = 0
(100 + -4x2 + -25x2 + 5x3 + -5x3 + x4) = 0

Combine like terms: -4x2 + -25x2 = -29x2
(100 + -29x2 + 5x3 + -5x3 + x4) = 0

Combine like terms: 5x3 + -5x3 = 0
(100 + -29x2 + 0 + x4) = 0
(100 + -29x2 + x4) = 0

Solving
100 + -29x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(25 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(25 + -1x2) = 0

Factor a difference between two squares.
((5 + x)(5 + -1x))(2 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {-2, 2, -5, 5}