144=(2x+16)(x+3)

Solution for 144=(2x+16)(x+3) equation:

Simplifying
144 = (2x + 16)(x + 3)

Reorder the terms:
144 = (16 + 2x)(x + 3)

Reorder the terms:
144 = (16 + 2x)(3 + x)

Multiply (16 + 2x) * (3 + x)
144 = (16(3 + x) + 2x * (3 + x))
144 = ((3 * 16 + x * 16) + 2x * (3 + x))
144 = ((48 + 16x) + 2x * (3 + x))
144 = (48 + 16x + (3 * 2x + x * 2x))
144 = (48 + 16x + (6x + 2x2))

Combine like terms: 16x + 6x = 22x
144 = (48 + 22x + 2x2)

Solving
144 = 48 + 22x + 2x2

Solving for variable 'x'.

Combine like terms: 144 + -48 = 96
96 + -22x + -2x2 = 48 + 22x + 2x2 + -48 + -22x + -2x2

Reorder the terms:
96 + -22x + -2x2 = 48 + -48 + 22x + -22x + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
96 + -22x + -2x2 = 0 + 22x + -22x + 2x2 + -2x2
96 + -22x + -2x2 = 22x + -22x + 2x2 + -2x2

Combine like terms: 22x + -22x = 0
96 + -22x + -2x2 = 0 + 2x2 + -2x2
96 + -22x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
96 + -22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -11x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(48 + -11x + -1x2)' equal to zero and attempt to solve:

Simplifying
48 + -11x + -1x2 = 0

Solving
48 + -11x + -1x2 = 0

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

Divide each side by '-1'.
-48 + 11x + x2 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 11x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 11x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 11x + x2 = 0 + 48
11x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
11x + x2 = 48

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 48 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 48 + 30.25

Combine like terms: 48 + 30.25 = 78.25
30.25 + 11x + x2 = 78.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 5.5) equal to 8.845903006 and -8.845903006.

Subproblem 1
x + 5.5 = 8.845903006

Simplifying
x + 5.5 = 8.845903006

Reorder the terms:
5.5 + x = 8.845903006

Solving
5.5 + x = 8.845903006

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 8.845903006 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 8.845903006 + -5.5
x = 8.845903006 + -5.5

Combine like terms: 8.845903006 + -5.5 = 3.345903006
x = 3.345903006

Simplifying
x = 3.345903006

Subproblem 2
x + 5.5 = -8.845903006

Simplifying
x + 5.5 = -8.845903006

Reorder the terms:
5.5 + x = -8.845903006

Solving
5.5 + x = -8.845903006

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -8.845903006 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -8.845903006 + -5.5
x = -8.845903006 + -5.5

Combine like terms: -8.845903006 + -5.5 = -14.345903006
x = -14.345903006

Simplifying
x = -14.345903006

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.345903006, -14.345903006}
Solution
x = {3.345903006, -14.345903006}