0=-x^2+14x-48

Solution for 0=-x^2+14x-48 equation:

Simplifying
0 = -1x2 + 14x + -48

Reorder the terms:
0 = -48 + 14x + -1x2

Solving
0 = -48 + 14x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 48 = 48
48 + -14x + x2 = -48 + 14x + -1x2 + 48 + -14x + x2

Reorder the terms:
48 + -14x + x2 = -48 + 48 + 14x + -14x + -1x2 + x2

Combine like terms: -48 + 48 = 0
48 + -14x + x2 = 0 + 14x + -14x + -1x2 + x2
48 + -14x + x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
48 + -14x + x2 = 0 + -1x2 + x2
48 + -14x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
48 + -14x + x2 = 0

Factor a trinomial.
(6 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {6, 8}