2(x^4-7)=9(x^2-1)

Solution for 2(x^4-7)=9(x^2-1) equation:

Simplifying
2(x4 + -7) = 9(x2 + -1)

Reorder the terms:
2(-7 + x4) = 9(x2 + -1)
(-7 * 2 + x4 * 2) = 9(x2 + -1)
(-14 + 2x4) = 9(x2 + -1)

Reorder the terms:
-14 + 2x4 = 9(-1 + x2)
-14 + 2x4 = (-1 * 9 + x2 * 9)
-14 + 2x4 = (-9 + 9x2)

Solving
-14 + 2x4 = -9 + 9x2

Solving for variable 'x'.

Reorder the terms:
-14 + 9 + -9x2 + 2x4 = -9 + 9x2 + 9 + -9x2

Combine like terms: -14 + 9 = -5
-5 + -9x2 + 2x4 = -9 + 9x2 + 9 + -9x2

Reorder the terms:
-5 + -9x2 + 2x4 = -9 + 9 + 9x2 + -9x2

Combine like terms: -9 + 9 = 0
-5 + -9x2 + 2x4 = 0 + 9x2 + -9x2
-5 + -9x2 + 2x4 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-5 + -9x2 + 2x4 = 0

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

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 + -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

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-2.236067978, 2.236067978}