10n^2-15n-60=10n

Solution for 10n^2-15n-60=10n equation:

Simplifying
10n2 + -15n + -60 = 10n

Reorder the terms:
-60 + -15n + 10n2 = 10n

Solving
-60 + -15n + 10n2 = 10n

Solving for variable 'n'.

Reorder the terms:
-60 + -15n + -10n + 10n2 = 10n + -10n

Combine like terms: -15n + -10n = -25n
-60 + -25n + 10n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-60 + -25n + 10n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -5n + 2n2) = 0

Factor a trinomial.
5((-3 + -2n)(4 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-1.5, 4}