=x^4-10x^2+9

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Solution for =x^4-10x^2+9 equation: 


Simplifying
0 = x4 + -10x2 + 9

Reorder the terms:
0 = 9 + -10x2 + x4

Solving
0 = 9 + -10x2 + x4

Solving for variable 'x'.

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

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

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

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

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

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

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

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


Subproblem 1
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 2
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 3
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 4
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
Solution
x = {-3, 3, -1, 1}

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