0=-16n+42-10n^2

Solution for 0=-16n+42-10n^2 equation:

Simplifying
0 = -16n + 42 + -10n2

Reorder the terms:
0 = 42 + -16n + -10n2

Solving
0 = 42 + -16n + -10n2

Solving for variable 'n'.

Combine like terms: 0 + -42 = -42
-42 + 16n + 10n2 = 42 + -16n + -10n2 + -42 + 16n + 10n2

Reorder the terms:
-42 + 16n + 10n2 = 42 + -42 + -16n + 16n + -10n2 + 10n2

Combine like terms: 42 + -42 = 0
-42 + 16n + 10n2 = 0 + -16n + 16n + -10n2 + 10n2
-42 + 16n + 10n2 = -16n + 16n + -10n2 + 10n2

Combine like terms: -16n + 16n = 0
-42 + 16n + 10n2 = 0 + -10n2 + 10n2
-42 + 16n + 10n2 = -10n2 + 10n2

Combine like terms: -10n2 + 10n2 = 0
-42 + 16n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 8n + 5n2) = 0

Factor a trinomial.
2((-3 + -1n)(7 + -5n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(7 + -5n)' equal to zero and attempt to solve:

Simplifying
7 + -5n = 0

Solving
7 + -5n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5n = 0 + -7
-5n = 0 + -7

Combine like terms: 0 + -7 = -7
-5n = -7

Divide each side by '-5'.
n = 1.4

Simplifying
n = 1.4
Solution
n = {-3, 1.4}