I have a chapter in my school course book on quadratic equations, in which we are learning how to solve nonquadratic-equations , by reducing them to quadratic form, the book describes 5 types of equations which can be solved by this method one of which is:

$$(x+a)(x+b)(x+c)(x+d)=k$$

According to the book to solve these kind of equations, we have to find which two pair of the above constants, which have the same sum eg $a+b=c+d$ Now we should rearrange the terms in the equation so as to get terms with one of the pair of constants adjacent to each other. eg if $a+c=b+d$ then we would rearrange as $$(x+a)(x+c)(x+b)(x+d)=k$$

Now after this step we would multiply the terms, constants of which form the pairs, with each other eg in above case $$(x^2+cx+ax+ac)(x^2+bx+dx+bd)=k$$

Now as we know $a+c=b+d$ we can place a variable say $y=x^2+cx+ax=x^2+bx+dx$ into the above equation and get $$(y+ac)(y+bd)=k$$ which could then be converted to a quadratic equation and then be solved as one, after which we could plug in value of $y$ and get the values of $x$ by applying an appropriate method. That being said, the book didn't give examples of the equations of the form $$(x+a)(ex+b)(ex+c)(x+d)=k$$ and has asked us to solve such type of an equation in the excercise, and i dont have a clue as how can i solve it, as the method of the book, described above cannot be applied to it. ANY HELP WOULD BE MUCH APPRECIATED

• Hi and welcome to the site. I helped you with typesetting your question. You can learn to do this on your own with LaTeX and MathJax and also see how others have typeset stuff. Commented Oct 4, 2015 at 13:22
• As @mathreadler said, use $MathJax$ while posting.
– user249332
Commented Oct 4, 2015 at 13:24
• If you write down the particular equation you need to solve, probably solutions will be posted quickly. Probably what you are expected to use is a mild variant of the idea described earlier. Commented Oct 4, 2015 at 13:28

since $e\ne 0$:
$$(x+a)(ex+b)(ex+c)(x+d)=k \iff$$ $$e^2\left(x+a\right)\left(x+\frac{b}{e}\right)\left(x+\frac{c}{e}\right)\left(x+d\right)=k \iff$$ $$\left(x+a\right)\left(x+\frac{b}{e}\right)\left(x+\frac{c}{e}\right)\left(x+d\right)=\frac{k}{e^2}$$