2x^4+216=42x^2

Solution for 2x^4+216=42x^2 equation:

Simplifying
2x4 + 216 = 42x2

Reorder the terms:
216 + 2x4 = 42x2

Solving
216 + 2x4 = 42x2

Solving for variable 'x'.

Reorder the terms:
216 + -42x2 + 2x4 = 42x2 + -42x2

Combine like terms: 42x2 + -42x2 = 0
216 + -42x2 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + -21x2 + x4) = 0

Factor a trinomial.
2((9 + -1x2)(12 + -1x2)) = 0

Factor a difference between two squares.
2(((3 + x)(3 + -1x))(12 + -1x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -1x2 = 0

Solving
12 + -1x2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x2 = 0 + -12
-1x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1x2 = -12

Divide each side by '-1'.
x2 = 12

Simplifying
x2 = 12

Take the square root of each side:
x = {-3.464101615, 3.464101615}
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

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

Simplifying
x = 3
Solution
x = {-3.464101615, 3.464101615, -3, 3}