2x^4=-7x^2+15

Solution for 2x^4=-7x^2+15 equation:

Simplifying
2x4 = -7x2 + 15

Reorder the terms:
2x4 = 15 + -7x2

Solving
2x4 = 15 + -7x2

Solving for variable 'x'.

Reorder the terms:
-15 + 7x2 + 2x4 = 15 + -7x2 + -15 + 7x2

Reorder the terms:
-15 + 7x2 + 2x4 = 15 + -15 + -7x2 + 7x2

Combine like terms: 15 + -15 = 0
-15 + 7x2 + 2x4 = 0 + -7x2 + 7x2
-15 + 7x2 + 2x4 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-15 + 7x2 + 2x4 = 0

Factor a trinomial.
(-5 + -1x2)(3 + -2x2) = 0

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

Simplifying
-5 + -1x2 = 0

Solving
-5 + -1x2 = 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 + -1x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x2 = 0 + 5
-1x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1x2 = 5

Divide each side by '-1'.
x2 = -5

Simplifying
x2 = -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 '(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

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.224744871, 1.224744871}