Question

(4x+3)(x+1)=1

Answer 1

(4x + 3)(x + 1) = 1
4x(x + 1) + 3(x + 1) = 1
4x^2 + 4x + 3x + 3 = 1
4x^2 + 7x + 3 = 1
4x^2 + 7x + 2 = 0

Answer 2

The first thing we need to do is un-factor this expression. For this, we do something known as the distributive property. This is a bit hard to explain, but basically what we do is this.

We have our equation. (4x+3)(x+1).

What we do is, we take apart one of these expressions. We're going to take apart (4x+3), but we could just as easily do it with (x+1). Then we re-arrange it in this fashion:

4x(x+1) + 3(x+1).

Basically, we're multiplying (4x+3) by (x+1), and this is the same thing as 4x times (x+1) + 3 times (x+1).

Now we simply multiply both these expressions as normal.

4x^2 + 4x + 3x + 3.
4x^2 + 7x + 3.

Now we have 4x^2 + 7x + 3 = 1. Let's turn that into a proper quadratic equation by removing 1 from both sides.

4x^2 + 7x + 2 = 0.

And now we have our quadratic equation! If you're not sure how to solve the question from here, reply and I'll show you how to solve a quadratic.