Solve the Equation: Finding m in 2(m+8)-3(16+m)=0

To solve the given equation $2(m+8) - 3(16+m) = 0$, we will follow these steps:

• Step 1: Apply the distributive property to expand the expression.
• Step 2: Combine like terms on both sides of the equation.
• Step 3: Solve for $m$ by isolating it.

Let's go through each step:

Step 1: Apply the distributive property:
Expand $2(m+8)$ to get $2m + 16$.
Expand $-3(16+m)$ to get $-48 - 3m$.

Step 2: Combine these expressions:
The equation becomes $2m + 16 - 48 - 3m = 0$.

Simplify it:
Combine like terms: $(2m - 3m) + (16 - 48)$.
This simplifies to $-m - 32 = 0$.

Step 3: Solve for $m$:
To isolate $m$, add 32 to both sides:
$-m = 32$.

Multiply both sides by -1 to solve for $m$:
$m = -32$.

Thus, the solution to the equation is $\mathbf{m = -32}$.