(x+2)(2)=(x+10)(x-7)

Solution for (x+2)(2)=(x+10)(x-7) equation:

Simplifying
(x + 2)(2) = (x + 10)(x + -7)

Reorder the terms:
(2 + x)(2) = (x + 10)(x + -7)

Reorder the terms for easier multiplication:
2(2 + x) = (x + 10)(x + -7)
(2 * 2 + x * 2) = (x + 10)(x + -7)
(4 + 2x) = (x + 10)(x + -7)

Reorder the terms:
4 + 2x = (10 + x)(x + -7)

Reorder the terms:
4 + 2x = (10 + x)(-7 + x)

Multiply (10 + x) * (-7 + x)
4 + 2x = (10(-7 + x) + x(-7 + x))
4 + 2x = ((-7 * 10 + x * 10) + x(-7 + x))
4 + 2x = ((-70 + 10x) + x(-7 + x))
4 + 2x = (-70 + 10x + (-7 * x + x * x))
4 + 2x = (-70 + 10x + (-7x + x2))

Combine like terms: 10x + -7x = 3x
4 + 2x = (-70 + 3x + x2)

Solving
4 + 2x = -70 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
4 + 70 + 2x + -3x + -1x2 = -70 + 3x + x2 + 70 + -3x + -1x2

Combine like terms: 4 + 70 = 74
74 + 2x + -3x + -1x2 = -70 + 3x + x2 + 70 + -3x + -1x2

Combine like terms: 2x + -3x = -1x
74 + -1x + -1x2 = -70 + 3x + x2 + 70 + -3x + -1x2

Reorder the terms:
74 + -1x + -1x2 = -70 + 70 + 3x + -3x + x2 + -1x2

Combine like terms: -70 + 70 = 0
74 + -1x + -1x2 = 0 + 3x + -3x + x2 + -1x2
74 + -1x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
74 + -1x + -1x2 = 0 + x2 + -1x2
74 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
74 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-74 + x + x2 = 0

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + x + x2 = 0 + 74
x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
x + x2 = 74

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 74 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 74 + 0.25

Combine like terms: 74 + 0.25 = 74.25
1.25 + x2 = 74.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.61684397 and -8.61684397.

Subproblem 1
x + 0.5 = 8.61684397

Simplifying
x + 0.5 = 8.61684397

Reorder the terms:
0.5 + x = 8.61684397

Solving
0.5 + x = 8.61684397

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 8.61684397 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 8.61684397 + -0.5
x = 8.61684397 + -0.5

Combine like terms: 8.61684397 + -0.5 = 8.11684397
x = 8.11684397

Simplifying
x = 8.11684397

Subproblem 2
x + 0.5 = -8.61684397

Simplifying
x + 0.5 = -8.61684397

Reorder the terms:
0.5 + x = -8.61684397

Solving
0.5 + x = -8.61684397

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -8.61684397 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -8.61684397 + -0.5
x = -8.61684397 + -0.5

Combine like terms: -8.61684397 + -0.5 = -9.11684397
x = -9.11684397

Simplifying
x = -9.11684397

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.11684397, -9.11684397}