-x^4+3x^2+4=6

Solution for -x^4+3x^2+4=6 equation:

Simplifying
-1x4 + 3x2 + 4 = 6

Reorder the terms:
4 + 3x2 + -1x4 = 6

Solving
4 + 3x2 + -1x4 = 6

Solving for variable 'x'.

Reorder the terms:
4 + -6 + 3x2 + -1x4 = 6 + -6

Combine like terms: 4 + -6 = -2
-2 + 3x2 + -1x4 = 6 + -6

Combine like terms: 6 + -6 = 0
-2 + 3x2 + -1x4 = 0

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

Factor a difference between two squares.
(-2 + x2)((1 + x)(1 + -1x)) = 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.414213562, 1.414213562, -1, 1}