2(-3+3x)+3(4-4x)=-42

Solution for 2(-3+3x)+3(4-4x)=-42 equation:

Simplifying
2(-3 + 3x) + 3(4 + -4x) = -42
(-3 * 2 + 3x * 2) + 3(4 + -4x) = -42
(-6 + 6x) + 3(4 + -4x) = -42
-6 + 6x + (4 * 3 + -4x * 3) = -42
-6 + 6x + (12 + -12x) = -42

Reorder the terms:
-6 + 12 + 6x + -12x = -42

Combine like terms: -6 + 12 = 6
6 + 6x + -12x = -42

Combine like terms: 6x + -12x = -6x
6 + -6x = -42

Solving
6 + -6x = -42

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + -6x = -42 + -6

Combine like terms: 6 + -6 = 0
0 + -6x = -42 + -6
-6x = -42 + -6

Combine like terms: -42 + -6 = -48
-6x = -48

Divide each side by '-6'.
x = 8

Simplifying
x = 8