If $f(x) = x^2+3x-5$ and $g(x) = 2x -3$, find $x$

Question

If $f(x) = x^2+3x-5$ and $g(x) = 2x -3$, find $x$.

According to the textbook, the solutions are $x = 1$ or $x=-2$

Here is the textbook question:

I would appreciate it if you could post the solution in a step by step form.

Thank You

Answer 1

Since you said the answer is $x=1$, $x=-2. \space$ I assume you mean $f(x)=g(x)$.

$$ x^2+3x−5 = 2x-3 $$ $$ x^2+x−2 = 0 $$ $$ (x-1)(x+2)=0 $$ $$ x-1=0 \space or \space x+2=0 $$ $$ x=1 \space or \space x=-2 $$