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