0=-x^2-8x+48

Solution for 0=-x^2-8x+48 equation:

Simplifying
0 = -1x2 + -8x + 48

Reorder the terms:
0 = 48 + -8x + -1x2

Solving
0 = 48 + -8x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -48 = -48
-48 + 8x + x2 = 48 + -8x + -1x2 + -48 + 8x + x2

Reorder the terms:
-48 + 8x + x2 = 48 + -48 + -8x + 8x + -1x2 + x2

Combine like terms: 48 + -48 = 0
-48 + 8x + x2 = 0 + -8x + 8x + -1x2 + x2
-48 + 8x + x2 = -8x + 8x + -1x2 + x2

Combine like terms: -8x + 8x = 0
-48 + 8x + x2 = 0 + -1x2 + x2
-48 + 8x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-48 + 8x + x2 = 0

Factor a trinomial.
(-12 + -1x)(4 + -1x) = 0

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

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

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