Solve for X: 3x+7+3x+5-x = 3(x-3)(x+3)+5x Linear-Quadratic Equation

To solve this problem, let's follow these steps:

• Step 1: Simplify the left-hand side of the equation:
  Combine like terms: $3x + 3x - x + 7 + 5 = 5x + 12$.
• Step 2: Expand and simplify the right-hand side:
  Apply the difference of squares: $3(x-3)(x+3) = 3(x^2 - 9)$.
  This simplifies to $3x^2 - 27$.
  Then add $5x$: $3x^2 - 27 + 5x$.
• Step 3: Equate both sides and solve for $x$:
  We have $5x + 12 = 3x^2 + 5x - 27$.
  Subtract $5x$ and 12 from both sides: $0 = 3x^2 - 39$.
  This simplifies to $3x^2 = 39$.
  Divide by 3: $x^2 = 13$.
  Taking the square root of both sides, we find $x = \pm\sqrt{13}$.

Therefore, the solution to the equation is $x = \pm\sqrt{13}$.