x^5+24x=11x^3

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Solution for x^5+24x=11x^3 equation: 


Simplifying
x5 + 24x = 11x3

Reorder the terms:
24x + x5 = 11x3

Solving
24x + x5 = 11x3

Solving for variable 'x'.

Reorder the terms:
24x + -11x3 + x5 = 11x3 + -11x3

Combine like terms: 11x3 + -11x3 = 0
24x + -11x3 + x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(24 + -11x2 + x4) = 0

Factor a trinomial.
x((3 + -1x2)(8 + -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 '(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}

Subproblem 3
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 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 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Solution
x = {0, -1.732050808, 1.732050808, -2.828427125, 2.828427125}

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