42=-6(-3n+6)+6(n-3)

Solution for 42=-6(-3n+6)+6(n-3) equation:

Simplifying
42 = -6(-3n + 6) + 6(n + -3)

Reorder the terms:
42 = -6(6 + -3n) + 6(n + -3)
42 = (6 * -6 + -3n * -6) + 6(n + -3)
42 = (-36 + 18n) + 6(n + -3)

Reorder the terms:
42 = -36 + 18n + 6(-3 + n)
42 = -36 + 18n + (-3 * 6 + n * 6)
42 = -36 + 18n + (-18 + 6n)

Reorder the terms:
42 = -36 + -18 + 18n + 6n

Combine like terms: -36 + -18 = -54
42 = -54 + 18n + 6n

Combine like terms: 18n + 6n = 24n
42 = -54 + 24n

Solving
42 = -54 + 24n

Solving for variable 'n'.

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

Add '-24n' to each side of the equation.
42 + -24n = -54 + 24n + -24n

Combine like terms: 24n + -24n = 0
42 + -24n = -54 + 0
42 + -24n = -54

Add '-42' to each side of the equation.
42 + -42 + -24n = -54 + -42

Combine like terms: 42 + -42 = 0
0 + -24n = -54 + -42
-24n = -54 + -42

Combine like terms: -54 + -42 = -96
-24n = -96

Divide each side by '-24'.
n = 4

Simplifying
n = 4