(x^2+4)(2x^2-7)=0

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Solution for (x^2+4)(2x^2-7)=0 equation:


Simplifying
(x2 + 4)(2x2 + -7) = 0

Reorder the terms:
(4 + x2)(2x2 + -7) = 0

Reorder the terms:
(4 + x2)(-7 + 2x2) = 0

Multiply (4 + x2) * (-7 + 2x2)
(4(-7 + 2x2) + x2(-7 + 2x2)) = 0
((-7 * 4 + 2x2 * 4) + x2(-7 + 2x2)) = 0
((-28 + 8x2) + x2(-7 + 2x2)) = 0
(-28 + 8x2 + (-7 * x2 + 2x2 * x2)) = 0
(-28 + 8x2 + (-7x2 + 2x4)) = 0

Combine like terms: 8x2 + -7x2 = 1x2
(-28 + 1x2 + 2x4) = 0

Solving
-28 + 1x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x2)(7 + -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 '(7 + -2x2)' equal to zero and attempt to solve:

Simplifying
7 + -2x2 = 0

Solving
7 + -2x2 = 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 + -2x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x2 = 0 + -7
-2x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-2x2 = -7

Divide each side by '-2'.
x2 = 3.5

Simplifying
x2 = 3.5

Take the square root of each side:
x = {-1.870828693, 1.870828693}
Solution
x = {-1.870828693, 1.870828693}

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