(4x-3)(3+4x)-2x(8x-1)=0

To solve the equation \((4x-3)(3+4x) - 2x(8x-1) = 0\), we first need to expand and simplify the expression. 1. **Expand \((4x-3)(3+4x)\)**: \[ (4x-3)(3+4x) = 4x \cdot 3 + 4x \cdot 4x - 3 \cdot 3 - 3 \cdot 4x \] \[ = 12x + 16x^2 - 9 - 12x \] \[ = 16x^2 - 9 \] 2. **Expand \(-2x(8x-1)\)**: \[ -2x(8x-1) = -2x \cdot 8x + 2x \cdot 1 \] \[ = -16x^2 + 2x \] 3. **Combine the two parts**: Now we combine \(16x^2 - 9\) and \(-16x^2 + 2x\): \[ 16x^2 - 9 - 16x^2 + 2x = 0 \] The \(16x^2\) terms cancel out: \[ 2x - 9 = 0 \] 4. **Solve for \(x\)**: \[ 2x = 9 \] \[ x = \frac{9}{2} \] Thus, the solution to the equation is: \[ \boxed{\frac{9}{2}} \]