(4-p)(2p+3)=19

Solution for (4-p)(2p+3)=19 equation:

Simplifying
(4 + -1p)(2p + 3) = 19

Reorder the terms:
(4 + -1p)(3 + 2p) = 19

Multiply (4 + -1p) * (3 + 2p)
(4(3 + 2p) + -1p * (3 + 2p)) = 19
((3 * 4 + 2p * 4) + -1p * (3 + 2p)) = 19
((12 + 8p) + -1p * (3 + 2p)) = 19
(12 + 8p + (3 * -1p + 2p * -1p)) = 19
(12 + 8p + (-3p + -2p2)) = 19

Combine like terms: 8p + -3p = 5p
(12 + 5p + -2p2) = 19

Solving
12 + 5p + -2p2 = 19

Solving for variable 'p'.

Reorder the terms:
12 + -19 + 5p + -2p2 = 19 + -19

Combine like terms: 12 + -19 = -7
-7 + 5p + -2p2 = 19 + -19

Combine like terms: 19 + -19 = 0
-7 + 5p + -2p2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
3.5 + -2.5p + p2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -2.5p + -3.5 + p2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -2.5p + p2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -2.5p + p2 = 0 + -3.5
-2.5p + p2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-2.5p + p2 = -3.5

The p term is -2.5p.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5p + 1.5625 + p2 = -3.5 + 1.5625

Reorder the terms:
1.5625 + -2.5p + p2 = -3.5 + 1.5625

Combine like terms: -3.5 + 1.5625 = -1.9375
1.5625 + -2.5p + p2 = -1.9375

Factor a perfect square on the left side:
(p + -1.25)(p + -1.25) = -1.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.