`(3(h+2)-4)/(6)=(h(7times2-5))/(2)`
In the equation above, what is the value of h?

Explanation

To solve the equation \((3(h+2)-4)/(6)=(h(7 \times 2-5))/(2)\), we will follow these steps:

### Step 1: Simplify both sides of the equation
Start by simplifying the left-hand side and the right-hand side.

**Left-hand side:**
\[ \frac{3(h+2) - 4}{6} \]
Distributing \(3\) inside the parentheses:
\[ = \frac{3h + 6 - 4}{6} = \frac{3h + 2}{6} \]

**Right-hand side:**
\[ \frac{h(7 \times 2 - 5)}{2} \]
Calculating \(7 \times 2\):
\[ = \frac{h(14 - 5)}{2} = \frac{h \cdot 9}{2} = \frac{9h}{2} \]

Now, we rewrite the equation:
\[ \frac{3h + 2}{6} = \frac{9h}{2} \]

### Step 2: Cross-multiply to eliminate the fractions
Cross-multiplying gives:
\[ 2(3h + 2) = 6(9h) \]

### Step 3: Distribute on both sides
Distributing on the left-hand side:
\[ 6h + 4 = 54h \]

### Step 4: Rearrange the equation
Now, we will move all terms involving \(h\) to one side and constant terms to the other side:
\[ 6h + 4 - 54h = 0 \]
This simplifies to:
\[ -48h + 4 = 0 \]

### Step 5: Solve for \(h\)
Rearranging gives:
\[ -48h = -4 \]
Dividing both sides by \(-48\):
\[ h = \frac{-4}{-48} = \frac{4}{48} = \frac{1}{12} \]

Thus, the value of \(h\) is:
\[ \boxed{\frac{1}{12}} \]

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