10n^2-75n+35=0

Solution for 10n^2-75n+35=0 equation:

Simplifying
10n2 + -75n + 35 = 0

Reorder the terms:
35 + -75n + 10n2 = 0

Solving
35 + -75n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -15n + 2n2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 0

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

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

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

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

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {0.5, 7}