Express solution in simplest radical form: $(4x-1)(3x+7) = (5x-1)(2x+3)$

Question

I need help with the problem. I'm in grade 11 math.

$(4x-1)(3x+7)=(5x-1)(2x+3)$

So far I think I have to factor it and I got $(12x^2+25x-7)=(10x^2-13x-3)$

Thanks!

Answer 1

You are almost there! Note first that the sign of $13x$ on the right side is positive, not negative. Let's move all of the terms to one side $$12x^2+25x-7-10x^2-13x+3=0$$Let's combine like terms$$2x^2+12x-4=0\to x^2+6x-2=0$$Finally, we use the quadratic formula to find the roots, which are$$x=\color{red}{-3\pm\sqrt{11}}$$

Answer 2

Whenever you have an equation, the best course of action is usually to collect all like terms; in this case, all like powers: This means, assemble the $12x^2$ and $10x^2$ on the different sides to one single $2x^2$ on the left-hand side, and so on. Doing so, you arrive that the equation $2x^2 +12x-4 = 0$. This is a kind of equation you have probably(?) seen before.