x^6=6x^3+16

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Solution for x^6=6x^3+16 equation: 


Simplifying
x6 = 6x3 + 16

Reorder the terms:
x6 = 16 + 6x3

Solving
x6 = 16 + 6x3

Solving for variable 'x'.

Reorder the terms:
-16 + -6x3 + x6 = 16 + 6x3 + -16 + -6x3

Reorder the terms:
-16 + -6x3 + x6 = 16 + -16 + 6x3 + -6x3

Combine like terms: 16 + -16 = 0
-16 + -6x3 + x6 = 0 + 6x3 + -6x3
-16 + -6x3 + x6 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
-16 + -6x3 + x6 = 0

Factor a trinomial.
(-2 + -1x3)(8 + -1x3) = 0


Subproblem 1
Set the factor '(-2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-2 + -1x3 = 0

Solving
-2 + -1x3 = 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 + -1x3 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x3 = 0 + 2
-1x3 = 0 + 2

Combine like terms: 0 + 2 = 2
-1x3 = 2

Divide each side by '-1'.
x3 = -2

Simplifying
x3 = -2

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 '(8 + -1x3)' equal to zero and attempt to solve:

Simplifying
8 + -1x3 = 0

Solving
8 + -1x3 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x3 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x3 = 0 + -8
-1x3 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x3 = -8

Divide each side by '-1'.
x3 = 8

Simplifying
x3 = 8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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