To solve this determinant, you can use the Laplace Expansion method. This method involves expanding the determinant along a row or column and breaking it down into smaller determinants until you reach a 2x2 determinant, which can be easily solved.
In this case, you can expand along the first row. This would give you the following expression:
detA = -2a * det(-2b, 2q+y, 2r+z, 3y, 3z) + 2p * det(2p+x, 2q+y, 2r+z, 3x, 3z) - 3x * det(2p+x, 2q+y, -2c, 3x, 3y)
Next, you can expand each of these smaller determinants along the first column to get rid of the variables in the first row. This would give you the following expressions:
detA = -2a * (-2b * det(2q+y, 2r+z, 3z) + 2q * det(2p+x, 2r+z, 3z) - 3z * det(2p+x, 2q+y, -2c)) + 2p * (2p * det(2q+y, 2r+z, 3z) - 2q * det(2p+x, 2r+z, 3z) + 3z * det(2p+x, 2q+y, -2c)) - 3x * (2p * det(2q+y, 2r+z, 3y) - 2q * det(2p+x, 2r+z, 3y) + 3y * det(2p+x, 2q+y, -2c))
Now, you can solve each of these smaller determinants using the formula for 2x2 determinants, which is ad-bc. For example, the first determinant would be:
det(2q+y, 2r+z, 3z) = (2q * 3z) - (3z * 2r+z) = 6q - 6z
Similarly, you can solve the other smaller determinants and substitute them back into the original expression. This would give you:
detA = -2a * (-2
