19-p(p-3)=2

Solution for 19-p(p-3)=2 equation:

Simplifying
19 + -1p(p + -3) = 2

Reorder the terms:
19 + -1p(-3 + p) = 2
19 + (-3 * -1p + p * -1p) = 2
19 + (3p + -1p2) = 2

Solving
19 + 3p + -1p2 = 2

Solving for variable 'p'.

Reorder the terms:
19 + -2 + 3p + -1p2 = 2 + -2

Combine like terms: 19 + -2 = 17
17 + 3p + -1p2 = 2 + -2

Combine like terms: 2 + -2 = 0
17 + 3p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + -3p + p2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -3p + 17 + p2 = 0 + 17

Reorder the terms:
-17 + 17 + -3p + p2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3p + p2 = 0 + 17
-3p + p2 = 0 + 17

Combine like terms: 0 + 17 = 17
-3p + p2 = 17

The p term is -3p.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3p + 2.25 + p2 = 17 + 2.25

Reorder the terms:
2.25 + -3p + p2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + -3p + p2 = 19.25

Factor a perfect square on the left side:
(p + -1.5)(p + -1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(p + -1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
p + -1.5 = 4.387482194

Simplifying
p + -1.5 = 4.387482194

Reorder the terms:
-1.5 + p = 4.387482194

Solving
-1.5 + p = 4.387482194

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = 4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = 4.387482194 + 1.5
p = 4.387482194 + 1.5

Combine like terms: 4.387482194 + 1.5 = 5.887482194
p = 5.887482194

Simplifying
p = 5.887482194

Subproblem 2
p + -1.5 = -4.387482194

Simplifying
p + -1.5 = -4.387482194

Reorder the terms:
-1.5 + p = -4.387482194

Solving
-1.5 + p = -4.387482194

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + p = -4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + p = -4.387482194 + 1.5
p = -4.387482194 + 1.5

Combine like terms: -4.387482194 + 1.5 = -2.887482194
p = -2.887482194

Simplifying
p = -2.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.887482194, -2.887482194}