x^2(x^2-9)+5=x^2-4

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Solution for x^2(x^2-9)+5=x^2-4 equation: 


Simplifying
x2(x2 + -9) + 5 = x2 + -4

Reorder the terms:
x2(-9 + x2) + 5 = x2 + -4
(-9 * x2 + x2 * x2) + 5 = x2 + -4
(-9x2 + x4) + 5 = x2 + -4

Reorder the terms:
5 + -9x2 + x4 = x2 + -4

Reorder the terms:
5 + -9x2 + x4 = -4 + x2

Solving
5 + -9x2 + x4 = -4 + x2

Solving for variable 'x'.

Reorder the terms:
5 + 4 + -9x2 + -1x2 + x4 = -4 + x2 + 4 + -1x2

Combine like terms: 5 + 4 = 9
9 + -9x2 + -1x2 + x4 = -4 + x2 + 4 + -1x2

Combine like terms: -9x2 + -1x2 = -10x2
9 + -10x2 + x4 = -4 + x2 + 4 + -1x2

Reorder the terms:
9 + -10x2 + x4 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
9 + -10x2 + x4 = 0 + x2 + -1x2
9 + -10x2 + x4 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + -10x2 + x4 = 0

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

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

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


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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {-1, 1, -3, 3}

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