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

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

Simplifying
(2x2 + -3)(x2 + 4) = 0

Reorder the terms:
(-3 + 2x2)(x2 + 4) = 0

Reorder the terms:
(-3 + 2x2)(4 + x2) = 0

Multiply (-3 + 2x2) * (4 + x2)
(-3(4 + x2) + 2x2 * (4 + x2)) = 0
((4 * -3 + x2 * -3) + 2x2 * (4 + x2)) = 0
((-12 + -3x2) + 2x2 * (4 + x2)) = 0
(-12 + -3x2 + (4 * 2x2 + x2 * 2x2)) = 0
(-12 + -3x2 + (8x2 + 2x4)) = 0

Combine like terms: -3x2 + 8x2 = 5x2
(-12 + 5x2 + 2x4) = 0

Solving
-12 + 5x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x2)(3 + -2x2) = 0

Subproblem 1
Set the factor '(-4 + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x2 = 0

Solving
-4 + -1x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x2 = 0 + 4
-1x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-1x2 = 4

Divide each side by '-1'.
x2 = -4

Simplifying
x2 = -4

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 '(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}
Solution
x = {-1.224744871, 1.224744871}