Solve for p: 6(5 + p) = 7(p + 6) - 5.

Step-by-step solution

1. 1

   Expand the left side. Distribute the $6$ over both terms:

   $6(5+p)=30+6p$

2. 2

   Expand the right side and fold in the loose constant. Distribute the $7$, then subtract $5$:

   $7(p+6)-5=7p+42-5=7p+37$

   Combining $42-5$ now, before moving anything across the equals sign, keeps the next step to a single operation.

3. 3

   Write the simplified equation.

   $30+6p=7p+37$

   Both sides contain $p$, so the terms must be gathered before $p$ can be read off.

4. 4

   Eliminate the smaller p term. Subtracting $6p$ (rather than $7p$) leaves the variable with coefficient $+1$, so no division will be needed at the end:

   $30=p+37$

5. 5

   Isolate p. Subtract $37$ from both sides:

   $30-37=p\qquad\Longrightarrow\qquad p=-7$

6. 6

   Verify in the original equation. Left: $6(5-7)=6(-2)=-12$. Right: $7(-7+6)-5=7(-1)-5=-7-5=-12$ ✓. Both sides give $-12$, so $p=-7$ is confirmed.