**Solving the Equation: Finding the Root**

In this article, we will solve the given equation and find its root:

**Equation:**

```
0.6(x-2) + 4.6 = 0
```

**Step-by-Step Solution**

### Step 1: Simplify the Equation

Let's simplify the equation by combining like terms:

```
0.6x - 1.2 + 4.6 = 0
```

### Step 2: Combine Constant Terms

Combine the constant terms:

```
0.6x - 1.2 + 4.6 = 0
0.6x + 3.4 = 0
```

### Step 3: Isolate the Variable (x)

Subtract 3.4 from both sides of the equation to isolate x:

```
0.6x = -3.4
```

### Step 4: Divide by the Coefficient

Divide both sides of the equation by the coefficient of x (0.6):

```
x = -3.4 / 0.6
x = -5.67
```

Therefore, the root of the equation is **x = -5.67**.

**Another Equation to Solve:**

Additionally, we are given another equation:

```
4(7+x) = 0
```

### Step 1: Expand the Equation

Expand the equation:

```
28 + 4x = 0
```

### Step 2: Isolate the Variable (x)

Subtract 28 from both sides of the equation to isolate x:

```
4x = -28
```

### Step 3: Divide by the Coefficient

Divide both sides of the equation by the coefficient of x (4):

```
x = -28 / 4
x = -7
```

Therefore, the root of the equation is **x = -7**.