Solve the equation `(x+2)(x+3)(x+8)xx(x+12)=4x^2dot`

Explanation

`(x + 2) (x + 3) (x + 8) (x + 12) = 4x^(2)`
or `{(x + 2) (x + 12)} {(x + 3) (x + 8)} = 4x^(2)`
or `(x^(2) + 14x+24) (x^(2) + 11x + 24) = 4x ^(2)`
Dividing throughout by `x^(2)`, we get
`(x + 14 + (24)/(x))(x + 11+ (24)/(x)) = 4`
`rArr (y + 14 ) (y + 11) = 4`, Where `x + (24)/(x) = y`
or `y^(2) + 25y + 154 = 4`
or ` y^(2) + 25y + 154 = 0`
or `( y + 15) (y + 10) = 0`
or `y = -15, -10`
If y = - 15, then
`x + (24)/(x) = - 15`
or `x^(2) + 15x + 24 = 0`
or `x = (-15pmsqrt(129))/(2)`
If y = - 10, then
or `x^(2) + 10x + 24 = 0`
or `(x + 4) (x + 6) = 0`
or x = -4, -6
Hence, the roots of the given equation are `-4, -6 ( -15 pmsqrt(129))//2`.