x^2(x^2-4)-26(x^2-4)=0

Solution for x^2(x^2-4)-26(x^2-4)=0 equation:

Simplifying
x2(x2 + -4) + -26(x2 + -4) = 0

Reorder the terms:
x2(-4 + x2) + -26(x2 + -4) = 0
(-4 * x2 + x2 * x2) + -26(x2 + -4) = 0
(-4x2 + x4) + -26(x2 + -4) = 0

Reorder the terms:
-4x2 + x4 + -26(-4 + x2) = 0
-4x2 + x4 + (-4 * -26 + x2 * -26) = 0
-4x2 + x4 + (104 + -26x2) = 0

Reorder the terms:
104 + -4x2 + -26x2 + x4 = 0

Combine like terms: -4x2 + -26x2 = -30x2
104 + -30x2 + x4 = 0

Solving
104 + -30x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(26 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(26 + -1x2) = 0

Subproblem 1
Set the factor '(26 + -1x2)' equal to zero and attempt to solve:

Simplifying
26 + -1x2 = 0

Solving
26 + -1x2 = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x2 = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x2 = 0 + -26
-1x2 = 0 + -26

Combine like terms: 0 + -26 = -26
-1x2 = -26

Divide each side by '-1'.
x2 = 26

Simplifying
x2 = 26

Take the square root of each side:
x = {-5.099019514, 5.099019514}
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5.099019514, 5.099019514, -2, 2}