Solve the Equation: Unravel the Quadratic (x+3)² + (2x-3)² = 5x(x-3/5)

Find a X given the following equation:

$(x+3)^2+(2x-3)^2=5x(x-\frac{3}{5})$

To solve this problem, let's expand and simplify each side of the given equation:

• Step 1: Expand the left side:
  • Expand $(x + 3)^2 = x^2 + 6x + 9$
  • Expand $(2x - 3)^2 = 4x^2 - 12x + 9$
  Combine them to get $x^2 + 6x + 9 + 4x^2 - 12x + 9 = 5x^2 - 6x + 18$.
• Step 2: Expand the right side:
  • Expand $5x(x - \frac{3}{5}) = 5x^2 - 3x$
• Step 3: Set the equations from both sides equal and simplify: $5x^2 - 6x + 18 = 5x^2 - 3x$
• Step 4: Subtract $5x^2$ from both sides: $-6x + 18 = -3x$
• Step 5: Simplify to: $-6x + 3x = -18$ or equivalently $-3x = -18$
• Step 6: Solve for $x$: $x = \frac{-18}{-3} = 6$

Therefore, the solution to the problem is $x = 6$.