4x^5=x^3(32x-60)

Solution for 4x^5=x^3(32x-60) equation:

Simplifying
4x5 = x3(32x + -60)

Reorder the terms:
4x5 = x3(-60 + 32x)
4x5 = (-60 * x3 + 32x * x3)
4x5 = (-60x3 + 32x4)

Solving
4x5 = -60x3 + 32x4

Solving for variable 'x'.

Reorder the terms:
60x3 + -32x4 + 4x5 = -60x3 + 32x4 + 60x3 + -32x4

Reorder the terms:
60x3 + -32x4 + 4x5 = -60x3 + 60x3 + 32x4 + -32x4

Combine like terms: -60x3 + 60x3 = 0
60x3 + -32x4 + 4x5 = 0 + 32x4 + -32x4
60x3 + -32x4 + 4x5 = 32x4 + -32x4

Combine like terms: 32x4 + -32x4 = 0
60x3 + -32x4 + 4x5 = 0

Factor out the Greatest Common Factor (GCF), '4x3'.
4x3(15 + -8x + x2) = 0

Factor a trinomial.
4x3((3 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

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 '(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
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

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

Simplifying
x = 5
Solution
x = {3, 5}