已知關於x的方程m(4x+5)+n(3x-4)=17x-2有無窮個解,求mn的值

已知關於x的方程m(4x+5)+n(3x-4)=17x-2有無窮個解,求mn的值

m(4x+5)+n(3x-4)=17x-2
(4m+3n-17)x=4n-5m-2
當4m+3n-17=4n-5m-2=0時,不論x何時取何值都成立
4m+3n-17=0(1)
4n-5m-2=0(2)
(1)*5+(2)*4
20m+15n-85+16n-20m-8=0
31n-93=0
n=3
m=(4n-2)/5=2
mn=6