10n^2-35=65n

Solution for 10n^2-35=65n equation:

Simplifying
10n2 + -35 = 65n

Reorder the terms:
-35 + 10n2 = 65n

Solving
-35 + 10n2 = 65n

Solving for variable 'n'.

Reorder the terms:
-35 + -65n + 10n2 = 65n + -65n

Combine like terms: 65n + -65n = 0
-35 + -65n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + -13n + 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}