0=-x^4+13x^2-36

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Solution for 0=-x^4+13x^2-36 equation: 


Simplifying
0 = -1x4 + 13x2 + -36

Reorder the terms:
0 = -36 + 13x2 + -1x4

Solving
0 = -36 + 13x2 + -1x4

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + -13x2 + x4 = -36 + 13x2 + -1x4 + 36 + -13x2 + x4

Reorder the terms:
36 + -13x2 + x4 = -36 + 36 + 13x2 + -13x2 + -1x4 + x4

Combine like terms: -36 + 36 = 0
36 + -13x2 + x4 = 0 + 13x2 + -13x2 + -1x4 + x4
36 + -13x2 + x4 = 13x2 + -13x2 + -1x4 + x4

Combine like terms: 13x2 + -13x2 = 0
36 + -13x2 + x4 = 0 + -1x4 + x4
36 + -13x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 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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