(x^2+3)=2x^2(x^2+7)

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

Simplifying
(x2 + 3) = 2x2(x2 + 7)

Reorder the terms:
(3 + x2) = 2x2(x2 + 7)

Remove parenthesis around (3 + x2)
3 + x2 = 2x2(x2 + 7)

Reorder the terms:
3 + x2 = 2x2(7 + x2)
3 + x2 = (7 * 2x2 + x2 * 2x2)
3 + x2 = (14x2 + 2x4)

Solving
3 + x2 = 14x2 + 2x4

Solving for variable 'x'.

Combine like terms: x2 + -14x2 = -13x2
3 + -13x2 + -2x4 = 14x2 + 2x4 + -14x2 + -2x4

Reorder the terms:
3 + -13x2 + -2x4 = 14x2 + -14x2 + 2x4 + -2x4

Combine like terms: 14x2 + -14x2 = 0
3 + -13x2 + -2x4 = 0 + 2x4 + -2x4
3 + -13x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
3 + -13x2 + -2x4 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + 6.5x2 + x4 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 6.5x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 6.5x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 6.5x2 + x4 = 0 + 1.5
6.5x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
6.5x2 + x4 = 1.5

The x term is 6.5x2.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x2 + 10.5625 + x4 = 1.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x2 + x4 = 1.5 + 10.5625

Combine like terms: 1.5 + 10.5625 = 12.0625
10.5625 + 6.5x2 + x4 = 12.0625

Factor a perfect square on the left side:
(x2 + 3.25)(x2 + 3.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x2 + 3.25) equal to 3.473110997 and -3.473110997.

Subproblem 1
x2 + 3.25 = 3.473110997

Simplifying
x2 + 3.25 = 3.473110997

Reorder the terms:
3.25 + x2 = 3.473110997

Solving
3.25 + x2 = 3.473110997

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x2 = 3.473110997 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x2 = 3.473110997 + -3.25
x2 = 3.473110997 + -3.25

Combine like terms: 3.473110997 + -3.25 = 0.223110997
x2 = 0.223110997

Simplifying
x2 = 0.223110997

Take the square root of each side:
x = {-0.472346268, 0.472346268}

Subproblem 2
x2 + 3.25 = -3.473110997

Simplifying
x2 + 3.25 = -3.473110997

Reorder the terms:
3.25 + x2 = -3.473110997

Solving
3.25 + x2 = -3.473110997

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x2 = -3.473110997 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x2 = -3.473110997 + -3.25
x2 = -3.473110997 + -3.25

Combine like terms: -3.473110997 + -3.25 = -6.723110997
x2 = -6.723110997

Simplifying
x2 = -6.723110997

Reorder the terms:
6.723110997 + x2 = -6.723110997 + 6.723110997

Combine like terms: -6.723110997 + 6.723110997 = 0.000000000
6.723110997 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.