To solve the systems of equations provided:

**c)**
1) \((x - 2)(6y + 1) = (2x - 3)(3y + 1)\)

2) \((2x + 1)(12y - 9) = (4x - 1)(6y - 5)\)

**d)**
1) \(3(y - 5) + 2(x - 3) = 0\)

2) \(7(x - 4) + 3(x + y - 1) - 14 = 0\)

Let's start with **c)**:

Expand both sides of each equation and simplify:

1) \((x - 2)(6y + 1) = 6xy + x - 12y - 2\)

\((2x - 3)(3y + 1) = 6xy + 2x - 9y - 3\)

Set the equations equal:
\[6xy + x - 12y - 2 = 6xy + 2x - 9y - 3\]

Simplify and collect like terms:
\[x - 12y - 2 = 2x - 9y - 3\]

This simplifies to:
\[-x = 3y - 1\]
\[x = -3y + 1\]

2) \((2x + 1)(12y - 9) = 24xy - 18x + 12y - 9\)

\((4x - 1)(6y - 5) = 24xy - 20x - 6y + 5\)

Set the equations equal:
\[24xy - 18x + 12y - 9 = 24xy - 20x - 6y + 5\]

Simplify and collect terms:
\[2x + 18y = 14\]

Now solve the system of equations:
1) \(x = -3y + 1\)
2) \(2x + 18y = 14\)

Substitute 1 into 2:
\[2(-3y + 1) + 18y = 14\]

\[-6y + 2 + 18y = 14\]

\[12y = 12\]

\[y = 1\]

Substitute \(y = 1\) into equation 1:
\[x = -3(1) + 1 = -2\]

Solution for **c)**: \(x = -2\), \(y = 1\)

Now let's solve **d)**:

1) \(3(y - 5) + 2(x - 3) = 0\)

\(3y - 15 + 2x - 6 = 0\)

\(2x + 3y = 21\)

2) \(7(x - 4) + 3(x + y - 1) - 14 = 0\)

\(7x - 28 + 3x + 3y - 3 - 14 = 0\)

\(10x + 3y - 45 = 0\)

\(10x + 3y = 45\)

Solve the system of equations:
1) \(2x + 3y = 21\)
2) \(10x + 3y = 45\)

Subtract equation 1 from equation 2:
\((10x + 3y) - (2x + 3y) = 45 - 21\)

\[8x = 24\]

\[x = 3\]

Substitute \(x = 3\) into equation 1:
\[2(3) + 3y = 21\]

\[6 + 3y = 21\]

\[3y = 15\]

\[y = 5\]

Solution for **d)**: \(x = 3\), \(y = 5\)