(x^2-2)(x^2-2)+3(x^2-2)=10

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Solution for (x^2-2)(x^2-2)+3(x^2-2)=10 equation: 


Simplifying
(x2 + -2)(x2 + -2) + 3(x2 + -2) = 10

Reorder the terms:
(-2 + x2)(x2 + -2) + 3(x2 + -2) = 10

Reorder the terms:
(-2 + x2)(-2 + x2) + 3(x2 + -2) = 10

Multiply (-2 + x2) * (-2 + x2)
(-2(-2 + x2) + x2(-2 + x2)) + 3(x2 + -2) = 10
((-2 * -2 + x2 * -2) + x2(-2 + x2)) + 3(x2 + -2) = 10
((4 + -2x2) + x2(-2 + x2)) + 3(x2 + -2) = 10
(4 + -2x2 + (-2 * x2 + x2 * x2)) + 3(x2 + -2) = 10
(4 + -2x2 + (-2x2 + x4)) + 3(x2 + -2) = 10

Combine like terms: -2x2 + -2x2 = -4x2
(4 + -4x2 + x4) + 3(x2 + -2) = 10

Reorder the terms:
4 + -4x2 + x4 + 3(-2 + x2) = 10
4 + -4x2 + x4 + (-2 * 3 + x2 * 3) = 10
4 + -4x2 + x4 + (-6 + 3x2) = 10

Reorder the terms:
4 + -6 + -4x2 + 3x2 + x4 = 10

Combine like terms: 4 + -6 = -2
-2 + -4x2 + 3x2 + x4 = 10

Combine like terms: -4x2 + 3x2 = -1x2
-2 + -1x2 + x4 = 10

Solving
-2 + -1x2 + x4 = 10

Solving for variable 'x'.

Reorder the terms:
-2 + -10 + -1x2 + x4 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + -1x2 + x4 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + -1x2 + x4 = 0

Factor a trinomial.
(-3 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-3 + -1x2)((2 + x)(2 + -1x)) = 0


Subproblem 1
Set the factor '(-3 + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + -1x2 = 0

Solving
-3 + -1x2 = 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 + -1x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x2 = 0 + 3
-1x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x2 = 3

Divide each side by '-1'.
x2 = -3

Simplifying
x2 = -3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
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 3
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
Solution
x = {-2, 2}

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