2x^5-23x^3+45x=0

Solution for 2x^5-23x^3+45x=0 equation:

Simplifying
2x5 + -23x3 + 45x = 0

Reorder the terms:
45x + -23x3 + 2x5 = 0

Solving
45x + -23x3 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(45 + -23x2 + 2x4) = 0

Factor a trinomial.
x((5 + -2x2)(9 + -1x2)) = 0

Factor a difference between two squares.
x((5 + -2x2)((3 + x)(3 + -1x))) = 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 '(5 + -2x2)' equal to zero and attempt to solve:

Simplifying
5 + -2x2 = 0

Solving
5 + -2x2 = 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 + -2x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x2 = 0 + -5
-2x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2x2 = -5

Divide each side by '-2'.
x2 = 2.5

Simplifying
x2 = 2.5

Take the square root of each side:
x = {-1.58113883, 1.58113883}
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 4
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -1.58113883, 1.58113883, -3, 3}