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

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

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

Reorder the terms:
x + 7(2 + x) = x(x + 10)
x + (2 * 7 + x * 7) = x(x + 10)
x + (14 + 7x) = x(x + 10)

Reorder the terms:
14 + x + 7x = x(x + 10)

Combine like terms: x + 7x = 8x
14 + 8x = x(x + 10)

Reorder the terms:
14 + 8x = x(10 + x)
14 + 8x = (10 * x + x * x)
14 + 8x = (10x + x2)

Solving
14 + 8x = 10x + x2

Solving for variable 'x'.

Combine like terms: 8x + -10x = -2x
14 + -2x + -1x2 = 10x + x2 + -10x + -1x2

Reorder the terms:
14 + -2x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
14 + -2x + -1x2 = 0 + x2 + -1x2
14 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-14 + 2x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 2x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 2x + x2 = 0 + 14

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 14 + 1

Reorder the terms:
1 + 2x + x2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + 2x + x2 = 15

Factor a perfect square on the left side:
(x + 1)(x + 1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 1) equal to 3.872983346 and -3.872983346.

Subproblem 1
x + 1 = 3.872983346

Simplifying
x + 1 = 3.872983346

Reorder the terms:
1 + x = 3.872983346

Solving
1 + x = 3.872983346

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.872983346 + -1
x = 3.872983346 + -1

Combine like terms: 3.872983346 + -1 = 2.872983346
x = 2.872983346

Simplifying
x = 2.872983346

Subproblem 2
x + 1 = -3.872983346

Simplifying
x + 1 = -3.872983346

Reorder the terms:
1 + x = -3.872983346

Solving
1 + x = -3.872983346

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.872983346 + -1
x = -3.872983346 + -1

Combine like terms: -3.872983346 + -1 = -4.872983346
x = -4.872983346

Simplifying
x = -4.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.872983346, -4.872983346}