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

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

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

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

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

Multiply (6 + 2x) * (4 + x)
(6(4 + x) + 2x * (4 + x)) = 0
((4 * 6 + x * 6) + 2x * (4 + x)) = 0
((24 + 6x) + 2x * (4 + x)) = 0
(24 + 6x + (4 * 2x + x * 2x)) = 0
(24 + 6x + (8x + 2x2)) = 0

Combine like terms: 6x + 8x = 14x
(24 + 14x + 2x2) = 0

Solving
24 + 14x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 7x + x2) = 0

Factor a trinomial.
2((4 + x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}