(3x+9)(2x-6)(x-4)(-x-4)=0

Solution for (3x+9)(2x-6)(x-4)(-x-4)=0 equation:

Simplifying
(3x + 9)(2x + -6)(x + -4)(-1x + -4) = 0

Reorder the terms:
(9 + 3x)(2x + -6)(x + -4)(-1x + -4) = 0

Reorder the terms:
(9 + 3x)(-6 + 2x)(x + -4)(-1x + -4) = 0

Reorder the terms:
(9 + 3x)(-6 + 2x)(-4 + x)(-1x + -4) = 0

Reorder the terms:
(9 + 3x)(-6 + 2x)(-4 + x)(-4 + -1x) = 0

Multiply (9 + 3x) * (-6 + 2x)
(9(-6 + 2x) + 3x * (-6 + 2x))(-4 + x)(-4 + -1x) = 0
((-6 * 9 + 2x * 9) + 3x * (-6 + 2x))(-4 + x)(-4 + -1x) = 0
((-54 + 18x) + 3x * (-6 + 2x))(-4 + x)(-4 + -1x) = 0
(-54 + 18x + (-6 * 3x + 2x * 3x))(-4 + x)(-4 + -1x) = 0
(-54 + 18x + (-18x + 6x2))(-4 + x)(-4 + -1x) = 0

Combine like terms: 18x + -18x = 0
(-54 + 0 + 6x2)(-4 + x)(-4 + -1x) = 0
(-54 + 6x2)(-4 + x)(-4 + -1x) = 0

Multiply (-54 + 6x2) * (-4 + x)
(-54(-4 + x) + 6x2 * (-4 + x))(-4 + -1x) = 0
((-4 * -54 + x * -54) + 6x2 * (-4 + x))(-4 + -1x) = 0
((216 + -54x) + 6x2 * (-4 + x))(-4 + -1x) = 0
(216 + -54x + (-4 * 6x2 + x * 6x2))(-4 + -1x) = 0
(216 + -54x + (-24x2 + 6x3))(-4 + -1x) = 0
(216 + -54x + -24x2 + 6x3)(-4 + -1x) = 0

Multiply (216 + -54x + -24x2 + 6x3) * (-4 + -1x)
(216(-4 + -1x) + -54x * (-4 + -1x) + -24x2 * (-4 + -1x) + 6x3 * (-4 + -1x)) = 0
((-4 * 216 + -1x * 216) + -54x * (-4 + -1x) + -24x2 * (-4 + -1x) + 6x3 * (-4 + -1x)) = 0
((-864 + -216x) + -54x * (-4 + -1x) + -24x2 * (-4 + -1x) + 6x3 * (-4 + -1x)) = 0
(-864 + -216x + (-4 * -54x + -1x * -54x) + -24x2 * (-4 + -1x) + 6x3 * (-4 + -1x)) = 0
(-864 + -216x + (216x + 54x2) + -24x2 * (-4 + -1x) + 6x3 * (-4 + -1x)) = 0
(-864 + -216x + 216x + 54x2 + (-4 * -24x2 + -1x * -24x2) + 6x3 * (-4 + -1x)) = 0
(-864 + -216x + 216x + 54x2 + (96x2 + 24x3) + 6x3 * (-4 + -1x)) = 0
(-864 + -216x + 216x + 54x2 + 96x2 + 24x3 + (-4 * 6x3 + -1x * 6x3)) = 0
(-864 + -216x + 216x + 54x2 + 96x2 + 24x3 + (-24x3 + -6x4)) = 0

Combine like terms: -216x + 216x = 0
(-864 + 0 + 54x2 + 96x2 + 24x3 + -24x3 + -6x4) = 0
(-864 + 54x2 + 96x2 + 24x3 + -24x3 + -6x4) = 0

Combine like terms: 54x2 + 96x2 = 150x2
(-864 + 150x2 + 24x3 + -24x3 + -6x4) = 0

Combine like terms: 24x3 + -24x3 = 0
(-864 + 150x2 + 0 + -6x4) = 0
(-864 + 150x2 + -6x4) = 0

Solving
-864 + 150x2 + -6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-144 + 25x2 + -1x4) = 0

Factor a trinomial.
6((-16 + x2)(9 + -1x2)) = 0

Factor a difference between two squares.
6(((4 + x)(-4 + x))(9 + -1x2)) = 0

Factor a difference between two squares.
6(((3 + x)(3 + -1x))(4 + x)(-4 + x)) = 0

Ignore the factor 6.
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 + 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 3
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 4
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
Solution
x = {-4, 4, -3, 3}