Solve: `2(3x-2)-3(4-5x)=7(1-2x)+12`

Answer

To solve the equation \( 2(3x - 2) - 3(4 - 5x) = 7(1 - 2x) + 12 \), we will follow these steps:

### Step 1: Expand the brackets
First, we will expand both sides of the equation.

\[ 2(3x - 2) = 6x - 4 \]
\[ -3(4 - 5x) = -12 + 15x \]
\[ 7(1 - 2x) = 7 - 14x \]

Substituting these into the equation gives us:

\[ 6x - 4 - 12 + 15x = 7 - 14x + 12 \]

### Step 2: Combine like terms
Now, we combine like terms on both sides.

Left side:
\[ 6x + 15x - 4 - 12 = 21x - 16 \]

Right side:
\[ 7 + 12 - 14x = 19 - 14x \]

So, the equation now looks like this:

\[ 21x - 16 = 19 - 14x \]

### Step 3: Move all terms involving \( x \) to one side
Next, we will move \( -14x \) to the left side and \( -16 \) to the right side.

Adding \( 14x \) to both sides:
\[ 21x + 14x = 19 + 16 \]

### Step 4: Simplify both sides
Now we simplify both sides:

Left side:
\[ 35x \]

Right side:
\[ 19 + 16 = 35 \]

So we have:
\[ 35x = 35 \]

### Step 5: Solve for \( x \)
Finally, we divide both sides by 35 to isolate \( x \):

\[ x = \frac{35}{35} = 1 \]

### Final Answer
Thus, the solution to the equation is:
\[ x = 1 \]

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