2(x+4)(6+x)=0

Solution for 2(x+4)(6+x)=0 equation:

Simplifying
2(x + 4)(6 + x) = 0

Reorder the terms:
2(4 + x)(6 + x) = 0

Multiply (4 + x) * (6 + x)
2(4(6 + x) + x(6 + x)) = 0
2((6 * 4 + x * 4) + x(6 + x)) = 0
2((24 + 4x) + x(6 + x)) = 0
2(24 + 4x + (6 * x + x * x)) = 0
2(24 + 4x + (6x + x2)) = 0

Combine like terms: 4x + 6x = 10x
2(24 + 10x + x2) = 0
(24 * 2 + 10x * 2 + x2 * 2) = 0
(48 + 20x + 2x2) = 0

Solving
48 + 20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 10x + x2) = 0

Factor a trinomial.
2((6 + x)(4 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {-6, -4}