3x^4+7x^2=76

Solution for 3x^4+7x^2=76 equation:

Simplifying
3x4 + 7x2 = 76

Reorder the terms:
7x2 + 3x4 = 76

Solving
7x2 + 3x4 = 76

Solving for variable 'x'.

Reorder the terms:
-76 + 7x2 + 3x4 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + 7x2 + 3x4 = 0

Factor a trinomial.
(-19 + -3x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-19 + -3x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-19 + -3x2)' equal to zero and attempt to solve:

Simplifying
-19 + -3x2 = 0

Solving
-19 + -3x2 = 0

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

Add '19' to each side of the equation.
-19 + 19 + -3x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3x2 = 0 + 19
-3x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-3x2 = 19

Divide each side by '-3'.
x2 = -6.333333333

Simplifying
x2 = -6.333333333

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}