6((2n^2)+3n-35)=0

Solution for 6((2n^2)+3n-35)=0 equation:

Simplifying
6((2n2) + 3n + -35) = 0

Reorder the terms:
6(-35 + 3n + (2n2)) = 0
(-35 * 6 + 3n * 6 + (2n2) * 6) = 0
(-210 + 18n + 12n2) = 0

Solving
-210 + 18n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-35 + 3n + 2n2) = 0

Factor a trinomial.
6((-5 + -1n)(7 + -2n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(7 + -2n)' equal to zero and attempt to solve:

Simplifying
7 + -2n = 0

Solving
7 + -2n = 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 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5
Solution
n = {-5, 3.5}