4n^2+10n-14=0

Solution for 4n^2+10n-14=0 equation:

Simplifying
4n2 + 10n + -14 = 0

Reorder the terms:
-14 + 10n + 4n2 = 0

Solving
-14 + 10n + 4n2 = 0

Solving for variable 'n'.

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

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

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

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Solution
n = {-3.5, 1}