4n^2-40n=-64

Solution for 4n^2-40n=-64 equation:

Simplifying
4n2 + -40n = -64

Reorder the terms:
-40n + 4n2 = -64

Solving
-40n + 4n2 = -64

Solving for variable 'n'.

Reorder the terms:
64 + -40n + 4n2 = -64 + 64

Combine like terms: -64 + 64 = 0
64 + -40n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -10n + n2) = 0

Factor a trinomial.
4((2 + -1n)(8 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

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

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

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

Simplifying
n = 8
Solution
n = {2, 8}