## Solving the Equation: (6a − )5a = a2 − 35a

This article will guide you through the steps to solve the equation **(6a − )5a = a2 − 35a**. We will simplify the equation and then use algebraic techniques to find the solutions for the variable 'a'.

### Step 1: Simplifying the Equation

Firstly, let's address the missing term in the equation. The expression "(6a − )" indicates a multiplication operation, implying there is a missing coefficient or variable to be multiplied by 6a.

**Assumption:** We will assume the missing term is a simple '1'. This assumption is based on the common occurrence of "1" being a hidden multiplier in algebraic expressions.

The equation becomes: **(6a - 1)5a = a2 - 35a**

### Step 2: Expanding the Left Side

Now we need to distribute the 5a on the left side of the equation:

(6a - 1)5a = 30a2 - 5a

### Step 3: Rearranging the Equation

Let's move all terms to one side of the equation to create a quadratic expression:

30a2 - 5a = a2 - 35a

30a2 - a2 - 5a + 35a = 0

29a2 + 30a = 0

### Step 4: Factoring the Quadratic Expression

The greatest common factor (GCF) for 29a2 and 30a is 'a'. Factoring out 'a' we get:

a(29a + 30) = 0

### Step 5: Solving for 'a'

For the product of two factors to equal zero, at least one of the factors must be zero. Therefore, we have two possible solutions:

**a = 0****29a + 30 = 0**

Solving the second equation for 'a':

29a = -30 a = -30/29

### Conclusion

The solutions to the equation (6a − )5a = a2 − 35a, assuming the missing term is '1', are:

**a = 0****a = -30/29**

Remember, this solution is based on the assumption of '1' being the missing term. If the missing term is different, the solutions will change accordingly.