e. $$ P(Q+6)=P-12 \quad $$ for $$ P $$

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$P$$:
  $$P\left(Q+6\right)=P-12$$
- step1: Rewrite the expression:
  $$\left(Q+6\right)P=P-12$$
- step2: Move the variable to the left side:
  $$\left(Q+6\right)P-P=-12$$
- step3: Subtract the terms:
  $$\left(Q+5\right)P=-12$$
- step4: Divide both sides:
  $$\frac{\left(Q+5\right)P}{Q+5}=\frac{-12}{Q+5}$$
- step5: Divide the numbers:
  $$P=-\frac{12}{Q+5}$$
To solve the equation $$ P(Q+6) = P - 12 $$ for $$ P $$, we can follow these steps:

1. **Distribute $$ P $$** on the left side:
   $$
   PQ + 6P = P - 12
   $$

2. **Rearrange the equation** to isolate terms involving $$ P $$:
   $$
   PQ + 6P - P = -12
   $$
   This simplifies to:
   $$
   PQ + 5P = -12
   $$

3. **Factor out $$ P $$** from the left side:
   $$
   P(Q + 5) = -12
   $$

4. **Solve for $$ P $$** by dividing both sides by $$ (Q + 5) $$:
   $$
   P = -\frac{12}{Q + 5}
   $$

Thus, the solution for $$ P $$ is:
$$
P = -\frac{12}{Q + 5}
$$
$$ P = -\frac{12}{Q + 5} $$

e. \( P(Q+6)=P-12 \quad \) for \( P \)

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