# Is there a way to solve a fourth grade equation if I know with which equations I got it?

So I have the multiplication of two quadratic equations that give me equal to a linear one, all with the same common variable. Am just trying to solve for that variable, but doing so with the resulting fourth grade equation is complicated and I need a method that doesn´t involve guessing, since most of what I´ve seen does that.

I had an idea based on factorizing. If one equation was equal to the result, the linear equation, and the other one to one, the result of their multiplication would end up being that linear equation. So then I set them equal to their respective numbers and then solved for the two possible answers that gave me the desired numbers.

However, this only works if the two results from one equation are also the results from the other equation, which is not always the case.

So am just where I started. One quadratic equation needs to give me a number that, multiplied by the number of the other equation, gives me the linear eq. (Which is the same, but wothout knowing the value of said numbers).

I don´t need anything special. I just need to solve for the variable, again without guessing.

Edit: Am sorry if am not wrting the equation, but I don´t exactly know how to use the formula type of letter (excuse me for my ignorance); but the equation is the one NeverEnoughTime wrote.

All the ways I see to solve the quartic equation are too complex and I don´t understand them. That´s why am asking if there´s a way to factorize it with the info I already have. Or if there´s a simple absolute formula for this scenario.

• What is the equation you want to solve? Commented Sep 22, 2020 at 0:56
• Yes, please just type up the equation to the best of your ability, using ^ to denote exponents. Commented Sep 22, 2020 at 0:57

I think you're asking to solve for $$x$$ here: $$(ax^2+bx+c)(dx^2+ex+f) = gx+h$$ which you can just solve with the quartic equation.