162=2(x+5)(x+2)

Solution for 162=2(x+5)(x+2) equation:

Simplifying
162 = 2(x + 5)(x + 2)

Reorder the terms:
162 = 2(5 + x)(x + 2)

Reorder the terms:
162 = 2(5 + x)(2 + x)

Multiply (5 + x) * (2 + x)
162 = 2(5(2 + x) + x(2 + x))
162 = 2((2 * 5 + x * 5) + x(2 + x))
162 = 2((10 + 5x) + x(2 + x))
162 = 2(10 + 5x + (2 * x + x * x))
162 = 2(10 + 5x + (2x + x2))

Combine like terms: 5x + 2x = 7x
162 = 2(10 + 7x + x2)
162 = (10 * 2 + 7x * 2 + x2 * 2)
162 = (20 + 14x + 2x2)

Solving
162 = 20 + 14x + 2x2

Solving for variable 'x'.

Combine like terms: 162 + -20 = 142
142 + -14x + -2x2 = 20 + 14x + 2x2 + -20 + -14x + -2x2

Reorder the terms:
142 + -14x + -2x2 = 20 + -20 + 14x + -14x + 2x2 + -2x2

Combine like terms: 20 + -20 = 0
142 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2
142 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
142 + -14x + -2x2 = 0 + 2x2 + -2x2
142 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
142 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(71 + -7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(71 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
71 + -7x + -1x2 = 0

Solving
71 + -7x + -1x2 = 0

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

Divide each side by '-1'.
-71 + 7x + x2 = 0

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + 7x + 71 + x2 = 0 + 71

Reorder the terms:
-71 + 71 + 7x + x2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 7x + x2 = 0 + 71
7x + x2 = 0 + 71

Combine like terms: 0 + 71 = 71
7x + x2 = 71

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 71 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 71 + 12.25

Combine like terms: 71 + 12.25 = 83.25
12.25 + 7x + x2 = 83.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 83.25

Calculate the square root of the right side: 9.124143795

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.124143795 and -9.124143795.

Subproblem 1
x + 3.5 = 9.124143795

Simplifying
x + 3.5 = 9.124143795

Reorder the terms:
3.5 + x = 9.124143795

Solving
3.5 + x = 9.124143795

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 9.124143795 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 9.124143795 + -3.5
x = 9.124143795 + -3.5

Combine like terms: 9.124143795 + -3.5 = 5.624143795
x = 5.624143795

Simplifying
x = 5.624143795

Subproblem 2
x + 3.5 = -9.124143795

Simplifying
x + 3.5 = -9.124143795

Reorder the terms:
3.5 + x = -9.124143795

Solving
3.5 + x = -9.124143795

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -9.124143795 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -9.124143795 + -3.5
x = -9.124143795 + -3.5

Combine like terms: -9.124143795 + -3.5 = -12.624143795
x = -12.624143795

Simplifying
x = -12.624143795

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.624143795, -12.624143795}
Solution
x = {5.624143795, -12.624143795}