Solve the equation and verify your answer: `(3x+5)/(4x+2)=(3x+4)/(4x+7)`

Explanation

`(3x+5)/(4x+2)=(3x+4)/(4x+7)`
`(3x+5)(4x+7)=(3x+4)(4x+2)`
`3x(4x+7)+5(4x+7)=3x(4x+2)+4(4x+2)`
`12x^2+21x+20x+35=12x^2+6x+16x+8`
`41x+35=22x+8`
`41x-22x=8-35`
`19x=-27`
`x=-27/19`
LHS
`(3(-27/19) +5) / (4(-27/19) + 2) = (3(-27/19) + 4) / (4(-27/19) + 7)`
` (-81/19 + 5) / (-108/19 + 2) = (-81/19 + 4) / (-108/19 + 7)`
` ((-81+95)/19) / ((-108+38)/19) = ((-81+76)/19) / ((-108+133)/19)`
`( 14/19) /( -70/19) = (-5/19) / (25/19)`
` -14/70 = -5/25`
` -1/5 = -1/5`
RHS=LHS