Solve the Equation: Unraveling 7a(3 + 1/a) - 2a = 0

To solve the equation $7a(3+\frac{1}{a})-2a=0$, follow these steps:

• Step 1: Distribute and Simplify

  Begin by distributing the $7a$ across the terms inside the parentheses:

  $7a(3+\frac{1}{a}) = 7a \times 3 + 7a \times \frac{1}{a}$

  This simplifies to:

  $21a + 7$

  Thus, the equation becomes:

  $21a + 7 - 2a = 0$

• Step 2: Combine Like Terms

  Combine the 'a' terms on the left side:

  $21a - 2a + 7 = 0$

  This simplifies to:

  $19a + 7 = 0$

• Step 3: Solve for $a$

  Rearrange the equation to solve for $a$:

  $19a = -7$

  Divide both sides by 19 to isolate $a$:

  $a = -\frac{7}{19}$

Therefore, the solution to the equation is $a = -\frac{7}{19}$.