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

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

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

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

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

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

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = 0

Solving
24 + 10x + x2 = 0

Solving for variable 'x'.

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

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}