7n^2+2n-5=0

Solution for 7n^2+2n-5=0 equation:

Simplifying
7n2 + 2n + -5 = 0

Reorder the terms:
-5 + 2n + 7n2 = 0

Solving
-5 + 2n + 7n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve:

Simplifying
5 + -7n = 0

Solving
5 + -7n = 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 + -7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7n = 0 + -5
-7n = 0 + -5

Combine like terms: 0 + -5 = -5
-7n = -5

Divide each side by '-7'.
n = 0.7142857143

Simplifying
n = 0.7142857143
Solution
n = {-1, 0.7142857143}