6n-9(5-n)=-12(n+6)

Solution for 6n-9(5-n)=-12(n+6) equation:

Simplifying
6n + -9(5 + -1n) = -12(n + 6)
6n + (5 * -9 + -1n * -9) = -12(n + 6)
6n + (-45 + 9n) = -12(n + 6)

Reorder the terms:
-45 + 6n + 9n = -12(n + 6)

Combine like terms: 6n + 9n = 15n
-45 + 15n = -12(n + 6)

Reorder the terms:
-45 + 15n = -12(6 + n)
-45 + 15n = (6 * -12 + n * -12)
-45 + 15n = (-72 + -12n)

Solving
-45 + 15n = -72 + -12n

Solving for variable 'n'.

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

Add '12n' to each side of the equation.
-45 + 15n + 12n = -72 + -12n + 12n

Combine like terms: 15n + 12n = 27n
-45 + 27n = -72 + -12n + 12n

Combine like terms: -12n + 12n = 0
-45 + 27n = -72 + 0
-45 + 27n = -72

Add '45' to each side of the equation.
-45 + 45 + 27n = -72 + 45

Combine like terms: -45 + 45 = 0
0 + 27n = -72 + 45
27n = -72 + 45

Combine like terms: -72 + 45 = -27
27n = -27

Divide each side by '27'.
n = -1

Simplifying
n = -1