2x^4-7x^2=-3

Solution for 2x^4-7x^2=-3 equation:

Simplifying
2x4 + -7x2 = -3

Reorder the terms:
-7x2 + 2x4 = -3

Solving
-7x2 + 2x4 = -3

Solving for variable 'x'.

Reorder the terms:
3 + -7x2 + 2x4 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -7x2 + 2x4 = 0

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

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

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x2 = 0 + -1
-2x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2x2 = -1

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-0.707106781, 0.707106781, -1.732050808, 1.732050808}