48=-x(x+16)

Solution for 48=-x(x+16) equation:

Simplifying
48 = -1x(x + 16)

Reorder the terms:
48 = -1x(16 + x)
48 = (16 * -1x + x * -1x)
48 = (-16x + -1x2)

Solving
48 = -16x + -1x2

Solving for variable 'x'.

Reorder the terms:
48 + 16x + x2 = -16x + 16x + -1x2 + x2

Combine like terms: -16x + 16x = 0
48 + 16x + x2 = 0 + -1x2 + x2
48 + 16x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
48 + 16x + x2 = 0

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

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
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 = {-12, -4}