2x^4-20=3x^2

Solution for 2x^4-20=3x^2 equation:

Simplifying
2x4 + -20 = 3x2

Reorder the terms:
-20 + 2x4 = 3x2

Solving
-20 + 2x4 = 3x2

Solving for variable 'x'.

Reorder the terms:
-20 + -3x2 + 2x4 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-20 + -3x2 + 2x4 = 0

Factor a trinomial.
(-5 + -2x2)(4 + -1x2) = 0

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

Subproblem 1
Set the factor '(-5 + -2x2)' equal to zero and attempt to solve:

Simplifying
-5 + -2x2 = 0

Solving
-5 + -2x2 = 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 + -2x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x2 = 0 + 5
-2x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2x2 = 5

Divide each side by '-2'.
x2 = -2.5

Simplifying
x2 = -2.5

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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}