2x^4+16x^2-4=9x^4

Solution for 2x^4+16x^2-4=9x^4 equation:

Simplifying
2x4 + 16x2 + -4 = 9x4

Reorder the terms:
-4 + 16x2 + 2x4 = 9x4

Solving
-4 + 16x2 + 2x4 = 9x4

Solving for variable 'x'.

Combine like terms: 2x4 + -9x4 = -7x4
-4 + 16x2 + -7x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
-4 + 16x2 + -7x4 = 0

Factor a trinomial.
(-2 + x2)(2 + -7x2) = 0

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

Simplifying
-2 + x2 = 0

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

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

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

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(2 + -7x2)' equal to zero and attempt to solve:

Simplifying
2 + -7x2 = 0

Solving
2 + -7x2 = 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 + -7x2 = 0 + -2

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

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

Divide each side by '-7'.
x2 = 0.2857142857

Simplifying
x2 = 0.2857142857

Take the square root of each side:
x = {-0.534522484, 0.534522484}
Solution
x = {-1.414213562, 1.414213562, -0.534522484, 0.534522484}