Giải phương trình
a, ( x - 2 ) ( x + 3 ) = 6
b, ( 2x - 3 ) ( x + 2 ) = 4
c, ( 3x - 4 ) ( 4 - x ) = 5
d, ( x + 3 ) ( x + 2 ) + ( x - 6 ) ( x + 2 ) = 4
e, ( 2x + 1 ) ( 4 - x ) - ( 5 - x ) ( 4 - x ) = 5
f, ( x - 4 ) ( x - 2 ) - ( x + 3 ) ( 3x - 1 ) = 7
g, ( 2x - 1 ) ( x + 4 ) - ( 2x - 3 )2 = 17
a) (x - 2)(x + 3) = 6
=> x2 + 3x - 2x - 6 = 6
=> x2 + x - 6 - 6 = 0
=> x2 + x - 12 = 0
=> x2 + 4x - 3x - 12 = 0
=> x(x + 4) - 3(x + 4) = 0
=> (x - 3)(x + 4) = 0
=> \(\orbr{\begin{cases}x-3=0\\x+4=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=3\\x=-4\end{cases}}\)
b) (2x - 3)(x + 2) = 4
=> 2x2 + 4x - 3x - 6 = 4
=> 2x2 + x - 6 - 4 = 0
=> 2x2 + x - 10 = 0
=> 2x2 + 5x - 4x - 10 = 0
=> x(2x + 5) - 2(2x + 5) = 0
=> (x - 2)(2x + 5) = 0
=> \(\orbr{\begin{cases}x-2=0\\2x+5=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=2\\x=-\frac{5}{2}\end{cases}}\)