4.05p+14.40=4.50p(p+3)

Solution for 4.05p+14.40=4.50p(p+3) equation:

Simplifying
4.05p + 14.40 = 4.50p(p + 3)

Reorder the terms:
14.40 + 4.05p = 4.50p(p + 3)

Reorder the terms:
14.40 + 4.05p = 4.50p(3 + p)
14.40 + 4.05p = (3 * 4.50p + p * 4.50p)
14.40 + 4.05p = (13.5p + 4.50p2)

Solving
14.40 + 4.05p = 13.5p + 4.50p2

Solving for variable 'p'.

Combine like terms: 4.05p + -13.5p = -9.45p
14.40 + -9.45p + -4.50p2 = 13.5p + 4.50p2 + -13.5p + -4.50p2

Reorder the terms:
14.40 + -9.45p + -4.50p2 = 13.5p + -13.5p + 4.50p2 + -4.50p2

Combine like terms: 13.5p + -13.5p = 0.0
14.40 + -9.45p + -4.50p2 = 0.0 + 4.50p2 + -4.50p2
14.40 + -9.45p + -4.50p2 = 4.50p2 + -4.50p2

Combine like terms: 4.50p2 + -4.50p2 = 0.00
14.40 + -9.45p + -4.50p2 = 0.00

Begin completing the square.  Divide all terms by
-4.50 the coefficient of the squared term: 

Divide each side by '-4.50'.
-3.2 + 2.1p + p2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 2.1p + 3.2 + p2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 2.1p + p2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 2.1p + p2 = 0 + 3.2
2.1p + p2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
2.1p + p2 = 3.2

The p term is 2.1p.  Take half its coefficient (1.05).
Square it (1.1025) and add it to both sides.

Add '1.1025' to each side of the equation.
2.1p + 1.1025 + p2 = 3.2 + 1.1025

Reorder the terms:
1.1025 + 2.1p + p2 = 3.2 + 1.1025

Combine like terms: 3.2 + 1.1025 = 4.3025
1.1025 + 2.1p + p2 = 4.3025

Factor a perfect square on the left side:
(p + 1.05)(p + 1.05) = 4.3025

Calculate the square root of the right side: 2.074246851

Break this problem into two subproblems by setting 
(p + 1.05) equal to 2.074246851 and -2.074246851.

Subproblem 1
p + 1.05 = 2.074246851

Simplifying
p + 1.05 = 2.074246851

Reorder the terms:
1.05 + p = 2.074246851

Solving
1.05 + p = 2.074246851

Solving for variable 'p'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + p = 2.074246851 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + p = 2.074246851 + -1.05
p = 2.074246851 + -1.05

Combine like terms: 2.074246851 + -1.05 = 1.024246851
p = 1.024246851

Simplifying
p = 1.024246851

Subproblem 2
p + 1.05 = -2.074246851

Simplifying
p + 1.05 = -2.074246851

Reorder the terms:
1.05 + p = -2.074246851

Solving
1.05 + p = -2.074246851

Solving for variable 'p'.

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

Add '-1.05' to each side of the equation.
1.05 + -1.05 + p = -2.074246851 + -1.05

Combine like terms: 1.05 + -1.05 = 0.00
0.00 + p = -2.074246851 + -1.05
p = -2.074246851 + -1.05

Combine like terms: -2.074246851 + -1.05 = -3.124246851
p = -3.124246851

Simplifying
p = -3.124246851

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.024246851, -3.124246851}