Solve: `3/2(2-4x)-4/5(3-2x)+(63)/5=0`

Answer

To solve the equation \( \frac{3}{2}(2-4x) - \frac{4}{5}(3-2x) + \frac{63}{5} = 0 \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the original equation:
\[ \frac{3}{2}(2-4x) - \frac{4}{5}(3-2x) + \frac{63}{5} = 0 \]

### Step 2: Find a common denominator
The denominators are 2 and 5. The least common multiple (LCM) of 2 and 5 is 10. We will multiply each term by 10 to eliminate the fractions:
\[ 10 \cdot \left(\frac{3}{2}(2-4x)\right) - 10 \cdot \left(\frac{4}{5}(3-2x)\right) + 10 \cdot \left(\frac{63}{5}\right) = 0 \]

### Step 3: Simplify each term
This gives us:
\[ 5 \cdot 3(2-4x) - 2 \cdot 4(3-2x) + 2 \cdot 63 = 0 \]
Simplifying each term:
\[ 15(2-4x) - 8(3-2x) + 126 = 0 \]

### Step 4: Distribute the terms
Now distribute:
\[ 30 - 60x - 24 + 16x + 126 = 0 \]

### Step 5: Combine like terms
Combine the constant terms and the \(x\) terms:
\[ (30 - 24 + 126) + (-60x + 16x) = 0 \]
This simplifies to:
\[ 132 - 44x = 0 \]

### Step 6: Isolate \(x\)
Now, isolate \(x\):
\[ -44x = -132 \]
Dividing both sides by -44:
\[ x = \frac{132}{44} \]

### Step 7: Simplify the fraction
Now simplify:
\[ x = 3 \]

### Final Answer
The solution to the equation is:
\[ x = 3 \]

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