Question

Despejar "a" en : d(a + bc)+b = b(a + 1)+c

Answer 1

d(a + bc)+b = b(a + 1)+c
ad + bcd + b = ab + b + c
ad - ab = b + c - bcd - b
a (d - b) = c - bcd
a = (c - bcd) /(d - b)

Answer 2

$d\left(a+bc\right)+b=b\left(a+1\right)+c$
$da+bcd+b=ba+b+c$
$da=-bcd+ba+c$
$da-ba=-bcd+c$
$\mathrm{Factorizar}\:da-ba:\quad a\left(d-b\right)$
$a\left(d-b\right)=-bcd+c$
$\mathrm{Dividir\:ambos\:lados\:entre\:}d-b;\quad \:d-b\ne \:0$
$\frac{a\left(d-b\right)}{d-b}=\frac{-bcd+c}{d-b}$
$a=\frac{-bcd+c}{d-b}$