To find how many solutions this equation has, we first simplify the equation.
Given equation is:
\(3(x+4) = -3x + 24\)
Expand the equation:
\(3x+12 = -3x + 24\)
Rearrange the terms to get the terms involving \(x\) on one side and constant on the other:
\(3x + 3x = 24 - 12\)
Simplify further:
\(6x = 12\)
Now solve for \(x\):
\(x = 12/6 = 2\)
Therefore, there is one unique solution for the equation, which is \(x = 2\).