78=-3(1-n)+5(4n+7)

Solution for 78=-3(1-n)+5(4n+7) equation:

Simplifying
78 = -3(1 + -1n) + 5(4n + 7)
78 = (1 * -3 + -1n * -3) + 5(4n + 7)
78 = (-3 + 3n) + 5(4n + 7)

Reorder the terms:
78 = -3 + 3n + 5(7 + 4n)
78 = -3 + 3n + (7 * 5 + 4n * 5)
78 = -3 + 3n + (35 + 20n)

Reorder the terms:
78 = -3 + 35 + 3n + 20n

Combine like terms: -3 + 35 = 32
78 = 32 + 3n + 20n

Combine like terms: 3n + 20n = 23n
78 = 32 + 23n

Solving
78 = 32 + 23n

Solving for variable 'n'.

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

Add '-23n' to each side of the equation.
78 + -23n = 32 + 23n + -23n

Combine like terms: 23n + -23n = 0
78 + -23n = 32 + 0
78 + -23n = 32

Add '-78' to each side of the equation.
78 + -78 + -23n = 32 + -78

Combine like terms: 78 + -78 = 0
0 + -23n = 32 + -78
-23n = 32 + -78

Combine like terms: 32 + -78 = -46
-23n = -46

Divide each side by '-23'.
n = 2

Simplifying
n = 2