3x^6=75x^4

Solution for 3x^6=75x^4 equation:

Simplifying
3x6 = 75x4

Solving
3x6 = 75x4

Solving for variable 'x'.

Reorder the terms:
-75x4 + 3x6 = 75x4 + -75x4

Combine like terms: 75x4 + -75x4 = 0
-75x4 + 3x6 = 0

Factor out the Greatest Common Factor (GCF), '3x4'.
3x4(-25 + x2) = 0

Factor a difference between two squares.
3x4((5 + x)(-5 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

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

Simplifying
-5 + x = 0

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

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

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

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