160=(x+3)(x+6)

Solution for 160=(x+3)(x+6) equation:

Simplifying
160 = (x + 3)(x + 6)

Reorder the terms:
160 = (3 + x)(x + 6)

Reorder the terms:
160 = (3 + x)(6 + x)

Multiply (3 + x) * (6 + x)
160 = (3(6 + x) + x(6 + x))
160 = ((6 * 3 + x * 3) + x(6 + x))
160 = ((18 + 3x) + x(6 + x))
160 = (18 + 3x + (6 * x + x * x))
160 = (18 + 3x + (6x + x2))

Combine like terms: 3x + 6x = 9x
160 = (18 + 9x + x2)

Solving
160 = 18 + 9x + x2

Solving for variable 'x'.

Combine like terms: 160 + -18 = 142
142 + -9x + -1x2 = 18 + 9x + x2 + -18 + -9x + -1x2

Reorder the terms:
142 + -9x + -1x2 = 18 + -18 + 9x + -9x + x2 + -1x2

Combine like terms: 18 + -18 = 0
142 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2
142 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
142 + -9x + -1x2 = 0 + x2 + -1x2
142 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
142 + -9x + -1x2 = 0

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

Divide each side by '-1'.
-142 + 9x + x2 = 0

Move the constant term to the right:

Add '142' to each side of the equation.
-142 + 9x + 142 + x2 = 0 + 142

Reorder the terms:
-142 + 142 + 9x + x2 = 0 + 142

Combine like terms: -142 + 142 = 0
0 + 9x + x2 = 0 + 142
9x + x2 = 0 + 142

Combine like terms: 0 + 142 = 142
9x + x2 = 142

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 142 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 142 + 20.25

Combine like terms: 142 + 20.25 = 162.25
20.25 + 9x + x2 = 162.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + 4.5) equal to 12.737739203 and -12.737739203.

Subproblem 1
x + 4.5 = 12.737739203

Simplifying
x + 4.5 = 12.737739203

Reorder the terms:
4.5 + x = 12.737739203

Solving
4.5 + x = 12.737739203

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 12.737739203 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 12.737739203 + -4.5
x = 12.737739203 + -4.5

Combine like terms: 12.737739203 + -4.5 = 8.237739203
x = 8.237739203

Simplifying
x = 8.237739203

Subproblem 2
x + 4.5 = -12.737739203

Simplifying
x + 4.5 = -12.737739203

Reorder the terms:
4.5 + x = -12.737739203

Solving
4.5 + x = -12.737739203

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -12.737739203 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -12.737739203 + -4.5
x = -12.737739203 + -4.5

Combine like terms: -12.737739203 + -4.5 = -17.237739203
x = -17.237739203

Simplifying
x = -17.237739203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.237739203, -17.237739203}