2x^2 -12x +p = q(x-r)^2 +10

To simplify and solve for p, we can expand the right side of the equation:

q(x-r)^2 + 10 = qx^2 - 2qxr + qr^2 + 10

Now we can equate the expanded form with the left side of the equation:

2x^2 - 12x + p = qx^2 - 2qxr + qr^2 + 10

To proceed, we will match the terms with the same power of x on both sides:

2x^2 = qx^2

This tells us that q = 2.

The term with x^2 on the left side is 0, while on the right side it is 2qxr. Since qx = 0, we can conclude that rx = 0, which means r = 0.

Now our equation becomes:

2x^2 - 12x + p = 2x^2 + 10

To solve for p, we can subtract 2x^2 from both sides and add 12x to both sides:

-12x + p = 10

Finally, we isolate p by subtracting 10 from both sides:

p = 10 - 12x

Therefore, the simplified form of the equation is p = 10 - 12x.