(x+8)(x+16)=0

Solution for (x+8)(x+16)=0 equation:

Simplifying
(x + 8)(x + 16) = 0

Reorder the terms:
(8 + x)(x + 16) = 0

Reorder the terms:
(8 + x)(16 + x) = 0

Multiply (8 + x) * (16 + x)
(8(16 + x) + x(16 + x)) = 0
((16 * 8 + x * 8) + x(16 + x)) = 0
((128 + 8x) + x(16 + x)) = 0
(128 + 8x + (16 * x + x * x)) = 0
(128 + 8x + (16x + x2)) = 0

Combine like terms: 8x + 16x = 24x
(128 + 24x + x2) = 0

Solving
128 + 24x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(16 + x)(8 + x) = 0

Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-16, -8}