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

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

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

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

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

Multiply (4 + 2x) * (6 + x)
(4(6 + x) + 2x * (6 + x)) = 0
((6 * 4 + x * 4) + 2x * (6 + x)) = 0
((24 + 4x) + 2x * (6 + x)) = 0
(24 + 4x + (6 * 2x + x * 2x)) = 0
(24 + 4x + (12x + 2x2)) = 0

Combine like terms: 4x + 12x = 16x
(24 + 16x + 2x2) = 0

Solving
24 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 8x + x2) = 0

Factor a trinomial.
2((6 + x)(2 + 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 '(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
Solution
x = {-6, -2}