2x^4-47x^2-75=0

Solution for 2x^4-47x^2-75=0 equation:

Simplifying
2x4 + -47x2 + -75 = 0

Reorder the terms:
-75 + -47x2 + 2x4 = 0

Solving
-75 + -47x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x2)(25 + -1x2) = 0

Factor a difference between two squares.
(-3 + -2x2)((5 + x)(5 + -1x)) = 0

Subproblem 1
Set the factor '(-3 + -2x2)' equal to zero and attempt to solve:

Simplifying
-3 + -2x2 = 0

Solving
-3 + -2x2 = 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 + -2x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x2 = 0 + 3
-2x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2x2 = 3

Divide each side by '-2'.
x2 = -1.5

Simplifying
x2 = -1.5

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 + -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 = {-5, 5}