42=2(x)*(x+7)+2

Solution for 42=2(x)*(x+7)+2 equation:

Simplifying
42 = 2(x)(x + 7) + 2

Reorder the terms:
42 = 2x(7 + x) + 2
42 = (7 * 2x + x * 2x) + 2
42 = (14x + 2x2) + 2

Reorder the terms:
42 = 2 + 14x + 2x2

Solving
42 = 2 + 14x + 2x2

Solving for variable 'x'.

Combine like terms: 42 + -2 = 40
40 + -14x + -2x2 = 2 + 14x + 2x2 + -2 + -14x + -2x2

Reorder the terms:
40 + -14x + -2x2 = 2 + -2 + 14x + -14x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
40 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2
40 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
40 + -14x + -2x2 = 0 + 2x2 + -2x2
40 + -14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + -14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + -7x + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + -7x + -1x2 = 0

Solving
20 + -7x + -1x2 = 0

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

Divide each side by '-1'.
-20 + 7x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 7x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 7x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 7x + x2 = 0 + 20
7x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
7x + x2 = 20

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 = 20 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 20 + 12.25

Combine like terms: 20 + 12.25 = 32.25
12.25 + 7x + x2 = 32.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
x + 3.5 = 5.678908346

Simplifying
x + 3.5 = 5.678908346

Reorder the terms:
3.5 + x = 5.678908346

Solving
3.5 + x = 5.678908346

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 = 5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.678908346 + -3.5
x = 5.678908346 + -3.5

Combine like terms: 5.678908346 + -3.5 = 2.178908346
x = 2.178908346

Simplifying
x = 2.178908346

Subproblem 2
x + 3.5 = -5.678908346

Simplifying
x + 3.5 = -5.678908346

Reorder the terms:
3.5 + x = -5.678908346

Solving
3.5 + x = -5.678908346

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 = -5.678908346 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.678908346 + -3.5
x = -5.678908346 + -3.5

Combine like terms: -5.678908346 + -3.5 = -9.178908346
x = -9.178908346

Simplifying
x = -9.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.178908346, -9.178908346}
Solution
x = {2.178908346, -9.178908346}