14n^2+35n-21=0

Solution for 14n^2+35n-21=0 equation:

Simplifying
14n2 + 35n + -21 = 0

Reorder the terms:
-21 + 35n + 14n2 = 0

Solving
-21 + 35n + 14n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 5n + 2n2) = 0

Factor a trinomial.
7((-3 + -1n)(1 + -2n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
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
Solution
n = {-3, 0.5}