5n+7(-6+n)=4(n+3)

Solution for 5n+7(-6+n)=4(n+3) equation:

Simplifying
5n + 7(-6 + n) = 4(n + 3)
5n + (-6 * 7 + n * 7) = 4(n + 3)
5n + (-42 + 7n) = 4(n + 3)

Reorder the terms:
-42 + 5n + 7n = 4(n + 3)

Combine like terms: 5n + 7n = 12n
-42 + 12n = 4(n + 3)

Reorder the terms:
-42 + 12n = 4(3 + n)
-42 + 12n = (3 * 4 + n * 4)
-42 + 12n = (12 + 4n)

Solving
-42 + 12n = 12 + 4n

Solving for variable 'n'.

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

Add '-4n' to each side of the equation.
-42 + 12n + -4n = 12 + 4n + -4n

Combine like terms: 12n + -4n = 8n
-42 + 8n = 12 + 4n + -4n

Combine like terms: 4n + -4n = 0
-42 + 8n = 12 + 0
-42 + 8n = 12

Add '42' to each side of the equation.
-42 + 42 + 8n = 12 + 42

Combine like terms: -42 + 42 = 0
0 + 8n = 12 + 42
8n = 12 + 42

Combine like terms: 12 + 42 = 54
8n = 54

Divide each side by '8'.
n = 6.75

Simplifying
n = 6.75