4x^5-20x^3=-24x

Solution for 4x^5-20x^3=-24x equation:

Simplifying
4x5 + -20x3 = -24x

Reorder the terms:
-20x3 + 4x5 = -24x

Solving
-20x3 + 4x5 = -24x

Solving for variable 'x'.

Reorder the terms:
24x + -20x3 + 4x5 = -24x + 24x

Combine like terms: -24x + 24x = 0
24x + -20x3 + 4x5 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(6 + -5x2 + x4) = 0

Factor a trinomial.
4x((2 + -1x2)(3 + -1x2)) = 0

Ignore the factor 4.
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 '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {0, -1.414213562, 1.414213562, -1.732050808, 1.732050808}