Step 1: Simplify the Left-Hand Side (LHS): Expand the LHS: (2x+5y)2−5(2x+5y)−14 Let z=2x+5y So, the equation becomes: z2−5z−14 Step 2: Factorize the Quadratic Expression: We need to factorize z2−5z−14 into the form (z+p)(z+q) To do this, we need to find two numbers whose product is -14 and whose sum is -5 . These numbers are -7 and 2 . Therefore, z2−5z−14 can be written as: (z−7)(z+2) Step 3: Substitute Back: Recall that z=2x+5y So, (z−7)(z+2) becomes: (2x+5y−7)(2x+5y+2) Step 4: Identify p and q : From the factorization, we have: p=−7 and q=2 Step 5: Calculate p+q : p+q=−7+2=−5