(3x^2-7)(x^2+1)=0

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Solution for (3x^2-7)(x^2+1)=0 equation: 


Simplifying
(3x2 + -7)(x2 + 1) = 0

Reorder the terms:
(-7 + 3x2)(x2 + 1) = 0

Reorder the terms:
(-7 + 3x2)(1 + x2) = 0

Multiply (-7 + 3x2) * (1 + x2)
(-7(1 + x2) + 3x2 * (1 + x2)) = 0
((1 * -7 + x2 * -7) + 3x2 * (1 + x2)) = 0
((-7 + -7x2) + 3x2 * (1 + x2)) = 0
(-7 + -7x2 + (1 * 3x2 + x2 * 3x2)) = 0
(-7 + -7x2 + (3x2 + 3x4)) = 0

Combine like terms: -7x2 + 3x2 = -4x2
(-7 + -4x2 + 3x4) = 0

Solving
-7 + -4x2 + 3x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x2)(7 + -3x2) = 0


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

Simplifying
-1 + -1x2 = 0

Solving
-1 + -1x2 = 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 + -1x2 = 0 + 1

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

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

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

Simplifying
x2 = -1

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 '(7 + -3x2)' equal to zero and attempt to solve:

Simplifying
7 + -3x2 = 0

Solving
7 + -3x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x2 = 0 + -7
-3x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-3x2 = -7

Divide each side by '-3'.
x2 = 2.333333333

Simplifying
x2 = 2.333333333

Take the square root of each side:
x = {-1.527525232, 1.527525232}
Solution
x = {-1.527525232, 1.527525232}

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