Solve for x. 2(x+2)-3(x-3)=x+7

Hello!
This is a linear equation for x. We'll see this if we open the parentheses using the distributive property:
2(x + 2) = 2x + 4,  3(x - 3) = 3x - 9,
so their difference is
2(x + 2) -3(x - 3) =2x + 4 - (3x - 9) = 2x + 4 - 3x + 9 =
= (2x - 3x) + (4 + 9) = -x + 13
(we grouped the terms with x and without x).
And this is equal to the right side,  -x + 13 = x + 7.
Add x to both sides and obtain 13 = 2x + 7, subtract 7 and obtain 6 = 2x. Finally, divide both sides by 2 and the answer is x = 3.