20n^2-64=64n

Solution for 20n^2-64=64n equation:

Simplifying
20n2 + -64 = 64n

Reorder the terms:
-64 + 20n2 = 64n

Solving
-64 + 20n2 = 64n

Solving for variable 'n'.

Reorder the terms:
-64 + -64n + 20n2 = 64n + -64n

Combine like terms: 64n + -64n = 0
-64 + -64n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -16n + 5n2) = 0

Factor a trinomial.
4((-4 + -5n)(4 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve:

Simplifying
-4 + -5n = 0

Solving
-4 + -5n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5n = 0 + 4
-5n = 0 + 4

Combine like terms: 0 + 4 = 4
-5n = 4

Divide each side by '-5'.
n = -0.8

Simplifying
n = -0.8
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-0.8, 4}