41n-42-5n^2=0

Solution for 41n-42-5n^2=0 equation:

Simplifying
41n + -42 + -5n2 = 0

Reorder the terms:
-42 + 41n + -5n2 = 0

Solving
-42 + 41n + -5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-7 + n)(6 + -5n) = 0

Subproblem 1
Set the factor '(-7 + n)' equal to zero and attempt to solve:

Simplifying
-7 + n = 0

Solving
-7 + n = 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 + n = 0 + 7

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

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

Simplifying
n = 7
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {7, 1.2}