(3x^2-972)(4x^2-5184)=0

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Solution for (3x^2-972)(4x^2-5184)=0 equation: 


Simplifying
(3x2 + -972)(4x2 + -5184) = 0

Reorder the terms:
(-972 + 3x2)(4x2 + -5184) = 0

Reorder the terms:
(-972 + 3x2)(-5184 + 4x2) = 0

Multiply (-972 + 3x2) * (-5184 + 4x2)
(-972(-5184 + 4x2) + 3x2 * (-5184 + 4x2)) = 0
((-5184 * -972 + 4x2 * -972) + 3x2 * (-5184 + 4x2)) = 0
((5038848 + -3888x2) + 3x2 * (-5184 + 4x2)) = 0
(5038848 + -3888x2 + (-5184 * 3x2 + 4x2 * 3x2)) = 0
(5038848 + -3888x2 + (-15552x2 + 12x4)) = 0

Combine like terms: -3888x2 + -15552x2 = -19440x2
(5038848 + -19440x2 + 12x4) = 0

Solving
5038848 + -19440x2 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(419904 + -1620x2 + x4) = 0

Factor a trinomial.
12((324 + -1x2)(1296 + -1x2)) = 0

Factor a difference between two squares.
12(((18 + x)(18 + -1x))(1296 + -1x2)) = 0

Factor a difference between two squares.
12(((36 + x)(36 + -1x))(18 + x)(18 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18

Subproblem 3
Set the factor '(36 + x)' equal to zero and attempt to solve:

Simplifying
36 + x = 0

Solving
36 + x = 0

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

Add '-36' to each side of the equation.
36 + -36 + x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + x = 0 + -36
x = 0 + -36

Combine like terms: 0 + -36 = -36
x = -36

Simplifying
x = -36

Subproblem 4
Set the factor '(36 + -1x)' equal to zero and attempt to solve:

Simplifying
36 + -1x = 0

Solving
36 + -1x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1x = 0 + -36
-1x = 0 + -36

Combine like terms: 0 + -36 = -36
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36
Solution
x = {-18, 18, -36, 36}

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