18. DETAILS MY NOTES AUFEXC4 9.4.017. \( \begin{array}{l}\text { First try to solve the equation by factoring. If you are unable to solve the equation by } \\ \text { the solution is not a real number, enter NOT REAL.) } \\ 6 x-10=3 x^{2}\end{array} \)

To solve the equation \(6x - 10 = 3x^2\) by factoring, first rearrange it into standard form: \(3x^2 - 6x + 10 = 0\). Then, simplify it to \(x^2 - 2x + \frac{10}{3} = 0\). To factor, look for two numbers that multiply to \(\frac{10}{3}\) and add to \(-2\). However, you'll find this isn't possible, indicating there are no real factors. Now, since factoring didn't work, you can use the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) where \(a=1\), \(b=-2\), and \(c=\frac{10}{3}\). Plugging in the values shows that the discriminant is negative, which means the solutions are not real numbers. So, the answer here is to enter "NOT REAL!"