(4-3x^2)(x^2+1)=2

Solution for (4-3x^2)(x^2+1)=2 equation:

Simplifying
(4 + -3x2)(x2 + 1) = 2

Reorder the terms:
(4 + -3x2)(1 + x2) = 2

Multiply (4 + -3x2) * (1 + x2)
(4(1 + x2) + -3x2 * (1 + x2)) = 2
((1 * 4 + x2 * 4) + -3x2 * (1 + x2)) = 2
((4 + 4x2) + -3x2 * (1 + x2)) = 2
(4 + 4x2 + (1 * -3x2 + x2 * -3x2)) = 2
(4 + 4x2 + (-3x2 + -3x4)) = 2

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

Solving
4 + 1x2 + -3x4 = 2

Solving for variable 'x'.

Reorder the terms:
4 + -2 + 1x2 + -3x4 = 2 + -2

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

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

Factor a trinomial.
(1 + -1x2)(2 + 3x2) = 0

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

Subproblem 1
Set the factor '(2 + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x2 = 0

Solving
2 + 3x2 = 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 + 3x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x2 = 0 + -2
3x2 = 0 + -2

Combine like terms: 0 + -2 = -2
3x2 = -2

Divide each side by '3'.
x2 = -0.6666666667

Simplifying
x2 = -0.6666666667

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 '(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, 1}