105=(7+x)(5+x)

Solution for 105=(7+x)(5+x) equation:

Simplifying
105 = (7 + x)(5 + x)

Multiply (7 + x) * (5 + x)
105 = (7(5 + x) + x(5 + x))
105 = ((5 * 7 + x * 7) + x(5 + x))
105 = ((35 + 7x) + x(5 + x))
105 = (35 + 7x + (5 * x + x * x))
105 = (35 + 7x + (5x + x2))

Combine like terms: 7x + 5x = 12x
105 = (35 + 12x + x2)

Solving
105 = 35 + 12x + x2

Solving for variable 'x'.

Combine like terms: 105 + -35 = 70
70 + -12x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Reorder the terms:
70 + -12x + -1x2 = 35 + -35 + 12x + -12x + x2 + -1x2

Combine like terms: 35 + -35 = 0
70 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
70 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
70 + -12x + -1x2 = 0 + x2 + -1x2
70 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
70 + -12x + -1x2 = 0

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

Divide each side by '-1'.
-70 + 12x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 12x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 12x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 12x + x2 = 0 + 70
12x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
12x + x2 = 70

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 70 + 36

Reorder the terms:
36 + 12x + x2 = 70 + 36

Combine like terms: 70 + 36 = 106
36 + 12x + x2 = 106

Factor a perfect square on the left side:
(x + 6)(x + 6) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 6) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + 6 = 10.295630141

Simplifying
x + 6 = 10.295630141

Reorder the terms:
6 + x = 10.295630141

Solving
6 + x = 10.295630141

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 10.295630141 + -6

Combine like terms: 6 + -6 = 0
0 + x = 10.295630141 + -6
x = 10.295630141 + -6

Combine like terms: 10.295630141 + -6 = 4.295630141
x = 4.295630141

Simplifying
x = 4.295630141

Subproblem 2
x + 6 = -10.295630141

Simplifying
x + 6 = -10.295630141

Reorder the terms:
6 + x = -10.295630141

Solving
6 + x = -10.295630141

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -10.295630141 + -6

Combine like terms: 6 + -6 = 0
0 + x = -10.295630141 + -6
x = -10.295630141 + -6

Combine like terms: -10.295630141 + -6 = -16.295630141
x = -16.295630141

Simplifying
x = -16.295630141

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.295630141, -16.295630141}