140n^2-192n+64=0

Solution for 140n^2-192n+64=0 equation:

Simplifying
140n2 + -192n + 64 = 0

Reorder the terms:
64 + -192n + 140n2 = 0

Solving
64 + -192n + 140n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -48n + 35n2) = 0

Factor a trinomial.
4((4 + -7n)(4 + -5n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(4 + -7n)' equal to zero and attempt to solve:

Simplifying
4 + -7n = 0

Solving
4 + -7n = 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 + -7n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7n = 0 + -4
-7n = 0 + -4

Combine like terms: 0 + -4 = -4
-7n = -4

Divide each side by '-7'.
n = 0.5714285714

Simplifying
n = 0.5714285714
Subproblem 2
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
Solution
n = {0.5714285714, 0.8}