0=-x^4+36x^2

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


Simplifying
0 = -1x4 + 36x2

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

Solving
0 = 36x2 + -1x4

Solving for variable 'x'.
Remove the zero:
-36x2 + x4 = 36x2 + -1x4 + -36x2 + x4

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

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

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

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-36 + x2) = 0

Factor a difference between two squares.
x2((6 + x)(-6 + x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

Subproblem 3
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, -6, 6}

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