0.5(-n^2+8n+48)=42

Solution for 0.5(-n^2+8n+48)=42 equation:

Simplifying
0.5(-1n2 + 8n + 48) = 42

Reorder the terms:
0.5(48 + 8n + -1n2) = 42
(48 * 0.5 + 8n * 0.5 + -1n2 * 0.5) = 42
(24 + 4n + -0.5n2) = 42

Solving
24 + 4n + -0.5n2 = 42

Solving for variable 'n'.

Reorder the terms:
24 + -42 + 4n + -0.5n2 = 42 + -42

Combine like terms: 24 + -42 = -18
-18 + 4n + -0.5n2 = 42 + -42

Combine like terms: 42 + -42 = 0
-18 + 4n + -0.5n2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
36 + -8n + n2 = 0

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -8n + -36 + n2 = 0 + -36

Reorder the terms:
36 + -36 + -8n + n2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -8n + n2 = 0 + -36
-8n + n2 = 0 + -36

Combine like terms: 0 + -36 = -36
-8n + n2 = -36

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = -36 + 16

Reorder the terms:
16 + -8n + n2 = -36 + 16

Combine like terms: -36 + 16 = -20
16 + -8n + n2 = -20

Factor a perfect square on the left side:
(n + -4)(n + -4) = -20

Can't calculate square root of the right side.

The solution to this equation could not be determined.