x^5-7x^3+9x=-x

Solution for x^5-7x^3+9x=-x equation:

Simplifying
x5 + -7x3 + 9x = -1x

Reorder the terms:
9x + -7x3 + x5 = -1x

Solving
9x + -7x3 + x5 = -1x

Solving for variable 'x'.

Reorder the terms:
9x + x + -7x3 + x5 = -1x + x

Combine like terms: 9x + x = 10x
10x + -7x3 + x5 = -1x + x

Combine like terms: -1x + x = 0
10x + -7x3 + x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + -7x2 + x4) = 0

Factor a trinomial.
x((2 + -1x2)(5 + -1x2)) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 3
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {0, -1.414213562, 1.414213562, -2.236067978, 2.236067978}