10n^2+35n-75=0

Solution for 10n^2+35n-75=0 equation:

Simplifying
10n2 + 35n + -75 = 0

Reorder the terms:
-75 + 35n + 10n2 = 0

Solving
-75 + 35n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + 7n + 2n2) = 0

Factor a trinomial.
5((-5 + -1n)(3 + -2n)) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-5, 1.5}