# Solving for a variable. Hard to do in this simple equation.

• Jon9992
In summary, the problem at hand is to solve for "a" in the equation a(a+b+c)=d. The solution involves using the distributive property to get a^2+ab+ac=d, and then dividing both sides by "a" to get a+b+c=d. From there, subtracting "a" and "d" yields b+c-d=-a. However, it is important to note that you cannot divide only one side of an equation, so the solution also involves using the Quadratic Formula to solve for "a".

#### Jon9992

Hi. This isn't for any sort of homework. I've run into a deadend where I have a situation like this where I need to solve for "a":

a(a+b+c) =d

You'd think it would be easy but I can't seem to get "a" by itself. It always end up on both sides of the equation at best which is starting to make me think it's somehow recursive. I know how to solve it if it didn't have the "c" by using the quadratic equation but not sure in this situation.

Thanks so much!

Last edited:
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d. Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.

Gbl911 said:
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d.
Absolutely not! You can't divide just one side of an equation. If you divide the left side by a, you have to also divide the right side by a.
Gb said:
Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.

After carrying out the multiplication on the left side, you get a2 + ab + ac = d. Add -d to both sides to get a2 + ab + ac - d = 0. One more step gets us to a2 + (b + c)a - d = 0. This is a quadratic in a, and can be solved for a by using the Quadratic Formula.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}