(5n^2+3n-2)+(2n^2-7n-1)=0

Solution for (5n^2+3n-2)+(2n^2-7n-1)=0 equation:

Simplifying
(5n2 + 3n + -2) + (2n2 + -7n + -1) = 0

Reorder the terms:
(-2 + 3n + 5n2) + (2n2 + -7n + -1) = 0

Remove parenthesis around (-2 + 3n + 5n2)
-2 + 3n + 5n2 + (2n2 + -7n + -1) = 0

Reorder the terms:
-2 + 3n + 5n2 + (-1 + -7n + 2n2) = 0

Remove parenthesis around (-1 + -7n + 2n2)
-2 + 3n + 5n2 + -1 + -7n + 2n2 = 0

Reorder the terms:
-2 + -1 + 3n + -7n + 5n2 + 2n2 = 0

Combine like terms: -2 + -1 = -3
-3 + 3n + -7n + 5n2 + 2n2 = 0

Combine like terms: 3n + -7n = -4n
-3 + -4n + 5n2 + 2n2 = 0

Combine like terms: 5n2 + 2n2 = 7n2
-3 + -4n + 7n2 = 0

Solving
-3 + -4n + 7n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-3 + -7n = 0

Solving
-3 + -7n = 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 + -7n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7n = 0 + 3
-7n = 0 + 3

Combine like terms: 0 + 3 = 3
-7n = 3

Divide each side by '-7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
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 = {-0.4285714286, 1}