10n^2+20n-36=-6

Solution for 10n^2+20n-36=-6 equation:

Simplifying
10n2 + 20n + -36 = -6

Reorder the terms:
-36 + 20n + 10n2 = -6

Solving
-36 + 20n + 10n2 = -6

Solving for variable 'n'.

Reorder the terms:
-36 + 6 + 20n + 10n2 = -6 + 6

Combine like terms: -36 + 6 = -30
-30 + 20n + 10n2 = -6 + 6

Combine like terms: -6 + 6 = 0
-30 + 20n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + 2n + n2) = 0

Factor a trinomial.
10((-3 + -1n)(1 + -1n)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
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, 1}