2[3(x-2)+5(x-3)]+x=-8

Solution for 2[3(x-2)+5(x-3)]+x=-8 equation:

Simplifying
2[3(x + -2) + 5(x + -3)] + x = -8

Reorder the terms:
2[3(-2 + x) + 5(x + -3)] + x = -8
2[(-2 * 3 + x * 3) + 5(x + -3)] + x = -8
2[(-6 + 3x) + 5(x + -3)] + x = -8

Reorder the terms:
2[-6 + 3x + 5(-3 + x)] + x = -8
2[-6 + 3x + (-3 * 5 + x * 5)] + x = -8
2[-6 + 3x + (-15 + 5x)] + x = -8

Reorder the terms:
2[-6 + -15 + 3x + 5x] + x = -8

Combine like terms: -6 + -15 = -21
2[-21 + 3x + 5x] + x = -8

Combine like terms: 3x + 5x = 8x
2[-21 + 8x] + x = -8
[-21 * 2 + 8x * 2] + x = -8
[-42 + 16x] + x = -8

Combine like terms: 16x + x = 17x
-42 + 17x = -8

Solving
-42 + 17x = -8

Solving for variable 'x'.

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

Add '42' to each side of the equation.
-42 + 42 + 17x = -8 + 42

Combine like terms: -42 + 42 = 0
0 + 17x = -8 + 42
17x = -8 + 42

Combine like terms: -8 + 42 = 34
17x = 34

Divide each side by '17'.
x = 2

Simplifying
x = 2