10n^2-36=-18n

Solution for 10n^2-36=-18n equation:

Simplifying
10n2 + -36 = -18n

Reorder the terms:
-36 + 10n2 = -18n

Solving
-36 + 10n2 = -18n

Solving for variable 'n'.

Reorder the terms:
-36 + 18n + 10n2 = -18n + 18n

Combine like terms: -18n + 18n = 0
-36 + 18n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 9n + 5n2) = 0

Factor a trinomial.
2((-3 + -1n)(6 + -5n)) = 0

Ignore the factor 2.
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 '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-3, 1.2}