x(x-8)+16(x+1)=0

Solution for x(x-8)+16(x+1)=0 equation:

Simplifying
x(x + -8) + 16(x + 1) = 0

Reorder the terms:
x(-8 + x) + 16(x + 1) = 0
(-8 * x + x * x) + 16(x + 1) = 0
(-8x + x2) + 16(x + 1) = 0

Reorder the terms:
-8x + x2 + 16(1 + x) = 0
-8x + x2 + (1 * 16 + x * 16) = 0
-8x + x2 + (16 + 16x) = 0

Reorder the terms:
16 + -8x + 16x + x2 = 0

Combine like terms: -8x + 16x = 8x
16 + 8x + x2 = 0

Solving
16 + 8x + x2 = 0

Solving for variable 'x'.

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

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 '(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 = {-4, -4}