5n^2+n-7=-3

Solution for 5n^2+n-7=-3 equation:

Simplifying
5n2 + n + -7 = -3

Reorder the terms:
-7 + n + 5n2 = -3

Solving
-7 + n + 5n2 = -3

Solving for variable 'n'.

Reorder the terms:
-7 + 3 + n + 5n2 = -3 + 3

Combine like terms: -7 + 3 = -4
-4 + n + 5n2 = -3 + 3

Combine like terms: -3 + 3 = 0
-4 + n + 5n2 = 0

Factor a trinomial.
(-1 + -1n)(4 + -5n) = 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 '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Solution
n = {-1, 0.8}