8x^4=30x^2-27

Solution for 8x^4=30x^2-27 equation:

Simplifying
8x4 = 30x2 + -27

Reorder the terms:
8x4 = -27 + 30x2

Solving
8x4 = -27 + 30x2

Solving for variable 'x'.

Reorder the terms:
27 + -30x2 + 8x4 = -27 + 30x2 + 27 + -30x2

Reorder the terms:
27 + -30x2 + 8x4 = -27 + 27 + 30x2 + -30x2

Combine like terms: -27 + 27 = 0
27 + -30x2 + 8x4 = 0 + 30x2 + -30x2
27 + -30x2 + 8x4 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
27 + -30x2 + 8x4 = 0

Factor a trinomial.
(3 + -2x2)(9 + -4x2) = 0

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

Subproblem 1
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}
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.224744871, 1.224744871, -1.5, 1.5}