Simplifying
3p^{2} + -12p + 63 = 0
Reorder the terms:
63 + -12p + 3p^{2} = 0
Solving
63 + -12p + 3p^{2} = 0
Solving for variable 'p'.
Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -4p + p^{2}) = 0
Ignore the factor 3.
#### Subproblem 1

Set the factor '(21 + -4p + p^{2})' equal to zero and attempt to solve:
Simplifying
21 + -4p + p^{2} = 0
Solving
21 + -4p + p^{2} = 0
Begin completing the square.
Move the constant term to the right:
Add '-21' to each side of the equation.
21 + -4p + -21 + p^{2} = 0 + -21
Reorder the terms:
21 + -21 + -4p + p^{2} = 0 + -21
Combine like terms: 21 + -21 = 0
0 + -4p + p^{2} = 0 + -21
-4p + p^{2} = 0 + -21
Combine like terms: 0 + -21 = -21
-4p + p^{2} = -21
The p term is -4p. Take half its coefficient (-2).
Square it (4) and add it to both sides.
Add '4' to each side of the equation.
-4p + 4 + p^{2} = -21 + 4
Reorder the terms:
4 + -4p + p^{2} = -21 + 4
Combine like terms: -21 + 4 = -17
4 + -4p + p^{2} = -17
Factor a perfect square on the left side:
(p + -2)(p + -2) = -17
Can't calculate square root of the right side.
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
The solution to this equation could not be determined.