(5x^2+1)(6x^2+4)=1

Solution for (5x^2+1)(6x^2+4)=1 equation:

Simplifying
(5x2 + 1)(6x2 + 4) = 1

Reorder the terms:
(1 + 5x2)(6x2 + 4) = 1

Reorder the terms:
(1 + 5x2)(4 + 6x2) = 1

Multiply (1 + 5x2) * (4 + 6x2)
(1(4 + 6x2) + 5x2 * (4 + 6x2)) = 1
((4 * 1 + 6x2 * 1) + 5x2 * (4 + 6x2)) = 1
((4 + 6x2) + 5x2 * (4 + 6x2)) = 1
(4 + 6x2 + (4 * 5x2 + 6x2 * 5x2)) = 1
(4 + 6x2 + (20x2 + 30x4)) = 1

Combine like terms: 6x2 + 20x2 = 26x2
(4 + 26x2 + 30x4) = 1

Solving
4 + 26x2 + 30x4 = 1

Solving for variable 'x'.

Reorder the terms:
4 + -1 + 26x2 + 30x4 = 1 + -1

Combine like terms: 4 + -1 = 3
3 + 26x2 + 30x4 = 1 + -1

Combine like terms: 1 + -1 = 0
3 + 26x2 + 30x4 = 0

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

Divide each side by '30'.
0.1 + 0.8666666667x2 + x4 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 0.8666666667x2 + -0.1 + x4 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + 0.8666666667x2 + x4 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 0.8666666667x2 + x4 = 0.0 + -0.1
0.8666666667x2 + x4 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
0.8666666667x2 + x4 = -0.1

The x term is 0.8666666667x2.  Take half its coefficient (0.4333333334).
Square it (0.1877777778) and add it to both sides.

Add '0.1877777778' to each side of the equation.
0.8666666667x2 + 0.1877777778 + x4 = -0.1 + 0.1877777778

Reorder the terms:
0.1877777778 + 0.8666666667x2 + x4 = -0.1 + 0.1877777778

Combine like terms: -0.1 + 0.1877777778 = 0.0877777778
0.1877777778 + 0.8666666667x2 + x4 = 0.0877777778

Factor a perfect square on the left side:
(x2 + 0.4333333334)(x2 + 0.4333333334) = 0.0877777778

Calculate the square root of the right side: 0.296273147

Break this problem into two subproblems by setting 
(x2 + 0.4333333334) equal to 0.296273147 and -0.296273147.

Subproblem 1
x2 + 0.4333333334 = 0.296273147

Simplifying
x2 + 0.4333333334 = 0.296273147

Reorder the terms:
0.4333333334 + x2 = 0.296273147

Solving
0.4333333334 + x2 = 0.296273147

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x2 = 0.296273147 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x2 = 0.296273147 + -0.4333333334
x2 = 0.296273147 + -0.4333333334

Combine like terms: 0.296273147 + -0.4333333334 = -0.1370601864
x2 = -0.1370601864

Simplifying
x2 = -0.1370601864

Reorder the terms:
0.1370601864 + x2 = -0.1370601864 + 0.1370601864

Combine like terms: -0.1370601864 + 0.1370601864 = 0.0000000000
0.1370601864 + x2 = 0.0000000000

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

Subproblem 2
x2 + 0.4333333334 = -0.296273147

Simplifying
x2 + 0.4333333334 = -0.296273147

Reorder the terms:
0.4333333334 + x2 = -0.296273147

Solving
0.4333333334 + x2 = -0.296273147

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x2 = -0.296273147 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x2 = -0.296273147 + -0.4333333334
x2 = -0.296273147 + -0.4333333334

Combine like terms: -0.296273147 + -0.4333333334 = -0.7296064804
x2 = -0.7296064804

Simplifying
x2 = -0.7296064804

Reorder the terms:
0.7296064804 + x2 = -0.7296064804 + 0.7296064804

Combine like terms: -0.7296064804 + 0.7296064804 = 0.0000000000
0.7296064804 + x2 = 0.0000000000

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.