(x^2-1)*(x^2-12)=-24

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Solution for (x^2-1)*(x^2-12)=-24 equation: 


Simplifying
(x2 + -1)(x2 + -12) = -24

Reorder the terms:
(-1 + x2)(x2 + -12) = -24

Reorder the terms:
(-1 + x2)(-12 + x2) = -24

Multiply (-1 + x2) * (-12 + x2)
(-1(-12 + x2) + x2(-12 + x2)) = -24
((-12 * -1 + x2 * -1) + x2(-12 + x2)) = -24
((12 + -1x2) + x2(-12 + x2)) = -24
(12 + -1x2 + (-12 * x2 + x2 * x2)) = -24
(12 + -1x2 + (-12x2 + x4)) = -24

Combine like terms: -1x2 + -12x2 = -13x2
(12 + -13x2 + x4) = -24

Solving
12 + -13x2 + x4 = -24

Solving for variable 'x'.

Reorder the terms:
12 + 24 + -13x2 + x4 = -24 + 24

Combine like terms: 12 + 24 = 36
36 + -13x2 + x4 = -24 + 24

Combine like terms: -24 + 24 = 0
36 + -13x2 + x4 = 0

Factor a trinomial.
(4 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(9 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -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 '(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 = {-2, 2, -3, 3}

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