X^4+3=13-9x^4

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Solution for X^4+3=13-9x^4 equation: 


Simplifying
X4 + 3 = 13 + -9x4

Reorder the terms:
3 + X4 = 13 + -9x4

Solving
3 + X4 = 13 + -9x4

Solving for variable 'X'.

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

Add '-3' to each side of the equation.
3 + -3 + X4 = 13 + -3 + -9x4

Combine like terms: 3 + -3 = 0
0 + X4 = 13 + -3 + -9x4
X4 = 13 + -3 + -9x4

Combine like terms: 13 + -3 = 10
X4 = 10 + -9x4

Simplifying
X4 = 10 + -9x4

Reorder the terms:
-10 + X4 + 9x4 = 10 + -9x4 + -10 + 9x4

Reorder the terms:
-10 + X4 + 9x4 = 10 + -10 + -9x4 + 9x4

Combine like terms: 10 + -10 = 0
-10 + X4 + 9x4 = 0 + -9x4 + 9x4
-10 + X4 + 9x4 = -9x4 + 9x4

Combine like terms: -9x4 + 9x4 = 0
-10 + X4 + 9x4 = 0

Factor a trinomial.
(X2 + -9x2)(X2 + -1x2) = 0

Factor a difference between two squares.
((X + 3x)(X + -3x))(X2 + -1x2) = 0

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


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

Simplifying
X + 3x = 0

Solving
X + 3x = 0

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

Add '-3x' to each side of the equation.
X + 3x + -3x = 0 + -3x

Combine like terms: 3x + -3x = 0
X + 0 = 0 + -3x
X = 0 + -3x
Remove the zero:
X = -3x

Simplifying
X = -3x

Subproblem 2
Set the factor '(X + -3x)' equal to zero and attempt to solve:

Simplifying
X + -3x = 0

Solving
X + -3x = 0

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

Add '3x' to each side of the equation.
X + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
X + 0 = 0 + 3x
X = 0 + 3x
Remove the zero:
X = 3x

Simplifying
X = 3x

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

Simplifying
X + x = 0

Solving
X + x = 0

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

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

Combine like terms: x + -1x = 0
X + 0 = 0 + -1x
X = 0 + -1x
Remove the zero:
X = -1x

Simplifying
X = -1x

Subproblem 4
Set the factor '(X + -1x)' equal to zero and attempt to solve:

Simplifying
X + -1x = 0

Solving
X + -1x = 0

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

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

Combine like terms: -1x + x = 0
X + 0 = 0 + x
X = 0 + x
Remove the zero:
X = x

Simplifying
X = x
Solution
X = {-3x, 3x, -1x, x}

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