(2x^4+8)-(6x^4+4)=0

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Solution for (2x^4+8)-(6x^4+4)=0 equation:


Simplifying
(2x4 + 8) + -1(6x4 + 4) = 0

Reorder the terms:
(8 + 2x4) + -1(6x4 + 4) = 0

Remove parenthesis around (8 + 2x4)
8 + 2x4 + -1(6x4 + 4) = 0

Reorder the terms:
8 + 2x4 + -1(4 + 6x4) = 0
8 + 2x4 + (4 * -1 + 6x4 * -1) = 0
8 + 2x4 + (-4 + -6x4) = 0

Reorder the terms:
8 + -4 + 2x4 + -6x4 = 0

Combine like terms: 8 + -4 = 4
4 + 2x4 + -6x4 = 0

Combine like terms: 2x4 + -6x4 = -4x4
4 + -4x4 = 0

Solving
4 + -4x4 = 0

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + -4x4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -4x4 = 0 + -4
-4x4 = 0 + -4

Combine like terms: 0 + -4 = -4
-4x4 = -4

Divide each side by '-4'.
x4 = 1

Simplifying
x4 = 1

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

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

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

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

Subproblem 1

Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 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 + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

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 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

Solution

x = {-1, 1}

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