Factor th is, \( 12 x^{2}+5 x-75=5 x \)

To factor the equation \( 12x^2 + 5x - 75 = 5x \), first simplify it by subtracting \( 5x \) from both sides, resulting in \( 12x^2 - 75 = 0 \). Now, you can factor out the greatest common factor, which is 3: \[ 3(4x^2 - 25) = 0 \] Recognizing that \( 4x^2 - 25 \) is a difference of squares, you can further factor this expression: \[ 3(2x - 5)(2x + 5) = 0 \] Now you have completely factored the original equation! Understanding the importance of factoring can help you avoid common mistakes in algebra. Many students jump straight into solving equations without simplifying first. Always look for a common factor before diving deeper into complicated equations. This approach saves time and leads to fewer errors! For those keen on mathematics, there are numerous resources that go deeper into factoring techniques. Books like "Algebra for Dummies" provide fun exercises, while online platforms like Khan Academy offer interactive lessons and practice problems to enhance your skills with factoring and polynomial expressions. Get ready to factor with flair!