(2)(x^2+108)+(2x)(2x-39)=0

Solution for (2)(x^2+108)+(2x)(2x-39)=0 equation:

Simplifying
(2)(x2 + 108) + (2x)(2x + -39) = 0

Reorder the terms:
2(108 + x2) + (2x)(2x + -39) = 0
(108 * 2 + x2 * 2) + (2x)(2x + -39) = 0
(216 + 2x2) + (2x)(2x + -39) = 0

Remove parenthesis around (2x)
216 + 2x2 + 2x(2x + -39) = 0

Reorder the terms:
216 + 2x2 + 2x(-39 + 2x) = 0
216 + 2x2 + (-39 * 2x + 2x * 2x) = 0
216 + 2x2 + (-78x + 4x2) = 0

Reorder the terms:
216 + -78x + 2x2 + 4x2 = 0

Combine like terms: 2x2 + 4x2 = 6x2
216 + -78x + 6x2 = 0

Solving
216 + -78x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(36 + -13x + x2) = 0

Factor a trinomial.
6((4 + -1x)(9 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}