Complete the Expression: (? + 5)(3a + ?) = 6ax + 15a - 16x - 40

Fill in the missing values:

$(?+5)(3a+?)=6ax+15a-16x-40$

To solve the problem of finding the missing values in the equation $(?+5)(3a+?)=6ax+15a-16x-40$, we need to expand the left side and equate the resulting expression with the right side.

Step-by-step solution:

• Step 1: Start by expanding $(?+5)(3a+?)$. Assume the missing values are $x$ and $b$ respectively, thus forming $(x+5)(3a+b)$.
• Step 2: Expand the expression on the left side:
  $(x+5)(3a+b) = x \cdot 3a + x \cdot b + 5 \cdot 3a + 5 \cdot b = 3ax + bx + 15a + 5b$.
• Step 3: Equate the expanded expression with the right side $6ax + 15a - 16x - 40$.

Upon comparing coefficients and constant terms:
- Coefficient of $ax$ should match: $3 = 6$. By substituting, $b = 2x$ to match terms.
- Constant term: $5b = -40$, therefore, solve for $b$. We find $b = -8$ because $5(-8) = -40$.

Once substitutions are made, verify that terms align. This shows:

• $x = -8$ (balancing constant $-40$) and substituting $b = 2x$ yields a consistent algebraic identity.

Therefore, the values that satisfy the equation are $(x, b) = (-8, 2x)$, confirming the answer $(-8, 2x)$. This choice best aligns when comparing the choices provided.