6x^4+19x^2+7x^2-26+12=0

Solution for 6x^4+19x^2+7x^2-26+12=0 equation:

Simplifying
6x4 + 19x2 + 7x2 + -26 + 12 = 0

Reorder the terms:
-26 + 12 + 19x2 + 7x2 + 6x4 = 0

Combine like terms: -26 + 12 = -14
-14 + 19x2 + 7x2 + 6x4 = 0

Combine like terms: 19x2 + 7x2 = 26x2
-14 + 26x2 + 6x4 = 0

Solving
-14 + 26x2 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 13x2 + 3x4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 13x2 + 3x4)' equal to zero and attempt to solve:

Simplifying
-7 + 13x2 + 3x4 = 0

Solving
-7 + 13x2 + 3x4 = 0

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

Divide each side by '3'.
-2.333333333 + 4.333333333x2 + x4 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 4.333333333x2 + 2.333333333 + x4 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 4.333333333x2 + x4 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 4.333333333x2 + x4 = 0 + 2.333333333
4.333333333x2 + x4 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
4.333333333x2 + x4 = 2.333333333

The x term is 4.333333333x2.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x2 + 4.694444446 + x4 = 2.333333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x2 + x4 = 2.333333333 + 4.694444446

Combine like terms: 2.333333333 + 4.694444446 = 7.027777779
4.694444446 + 4.333333333x2 + x4 = 7.027777779

Factor a perfect square on the left side:
(x2 + 2.166666667)(x2 + 2.166666667) = 7.027777779

Calculate the square root of the right side: 2.65099562

Break this problem into two subproblems by setting 
(x2 + 2.166666667) equal to 2.65099562 and -2.65099562.

Subproblem 1
x2 + 2.166666667 = 2.65099562

Simplifying
x2 + 2.166666667 = 2.65099562

Reorder the terms:
2.166666667 + x2 = 2.65099562

Solving
2.166666667 + x2 = 2.65099562

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x2 = 2.65099562 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x2 = 2.65099562 + -2.166666667
x2 = 2.65099562 + -2.166666667

Combine like terms: 2.65099562 + -2.166666667 = 0.484328953
x2 = 0.484328953

Simplifying
x2 = 0.484328953

Take the square root of each side:
x = {-0.695937463, 0.695937463}

Subproblem 2
x2 + 2.166666667 = -2.65099562

Simplifying
x2 + 2.166666667 = -2.65099562

Reorder the terms:
2.166666667 + x2 = -2.65099562

Solving
2.166666667 + x2 = -2.65099562

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x2 = -2.65099562 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x2 = -2.65099562 + -2.166666667
x2 = -2.65099562 + -2.166666667

Combine like terms: -2.65099562 + -2.166666667 = -4.817662287
x2 = -4.817662287

Simplifying
x2 = -4.817662287

Reorder the terms:
4.817662287 + x2 = -4.817662287 + 4.817662287

Combine like terms: -4.817662287 + 4.817662287 = 0.000000000
4.817662287 + 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.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.