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

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

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

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

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

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

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

Multiply (-5 + x) * (2 + x)
(-5(2 + x) + x(2 + x))(5 + x)(-2 + x) = 0
((2 * -5 + x * -5) + x(2 + x))(5 + x)(-2 + x) = 0
((-10 + -5x) + x(2 + x))(5 + x)(-2 + x) = 0
(-10 + -5x + (2 * x + x * x))(5 + x)(-2 + x) = 0
(-10 + -5x + (2x + x2))(5 + x)(-2 + x) = 0

Combine like terms: -5x + 2x = -3x
(-10 + -3x + x2)(5 + x)(-2 + x) = 0

Multiply (-10 + -3x + x2) * (5 + x)
(-10(5 + x) + -3x * (5 + x) + x2(5 + x))(-2 + x) = 0
((5 * -10 + x * -10) + -3x * (5 + x) + x2(5 + x))(-2 + x) = 0
((-50 + -10x) + -3x * (5 + x) + x2(5 + x))(-2 + x) = 0
(-50 + -10x + (5 * -3x + x * -3x) + x2(5 + x))(-2 + x) = 0
(-50 + -10x + (-15x + -3x2) + x2(5 + x))(-2 + x) = 0
(-50 + -10x + -15x + -3x2 + (5 * x2 + x * x2))(-2 + x) = 0
(-50 + -10x + -15x + -3x2 + (5x2 + x3))(-2 + x) = 0

Combine like terms: -10x + -15x = -25x
(-50 + -25x + -3x2 + 5x2 + x3)(-2 + x) = 0

Combine like terms: -3x2 + 5x2 = 2x2
(-50 + -25x + 2x2 + x3)(-2 + x) = 0

Multiply (-50 + -25x + 2x2 + x3) * (-2 + x)
(-50(-2 + x) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0
((-2 * -50 + x * -50) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0
((100 + -50x) + -25x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0
(100 + -50x + (-2 * -25x + x * -25x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0
(100 + -50x + (50x + -25x2) + 2x2 * (-2 + x) + x3(-2 + x)) = 0
(100 + -50x + 50x + -25x2 + (-2 * 2x2 + x * 2x2) + x3(-2 + x)) = 0
(100 + -50x + 50x + -25x2 + (-4x2 + 2x3) + x3(-2 + x)) = 0
(100 + -50x + 50x + -25x2 + -4x2 + 2x3 + (-2 * x3 + x * x3)) = 0
(100 + -50x + 50x + -25x2 + -4x2 + 2x3 + (-2x3 + x4)) = 0

Combine like terms: -50x + 50x = 0
(100 + 0 + -25x2 + -4x2 + 2x3 + -2x3 + x4) = 0
(100 + -25x2 + -4x2 + 2x3 + -2x3 + x4) = 0

Combine like terms: -25x2 + -4x2 = -29x2
(100 + -29x2 + 2x3 + -2x3 + x4) = 0

Combine like terms: 2x3 + -2x3 = 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}