x(x+6)=4(x+4)

Solution for x(x+6)=4(x+4) equation:

Simplifying
x(x + 6) = 4(x + 4)

Reorder the terms:
x(6 + x) = 4(x + 4)
(6 * x + x * x) = 4(x + 4)
(6x + x2) = 4(x + 4)

Reorder the terms:
6x + x2 = 4(4 + x)
6x + x2 = (4 * 4 + x * 4)
6x + x2 = (16 + 4x)

Solving
6x + x2 = 16 + 4x

Solving for variable 'x'.

Reorder the terms:
-16 + 6x + -4x + x2 = 16 + 4x + -16 + -4x

Combine like terms: 6x + -4x = 2x
-16 + 2x + x2 = 16 + 4x + -16 + -4x

Reorder the terms:
-16 + 2x + x2 = 16 + -16 + 4x + -4x

Combine like terms: 16 + -16 = 0
-16 + 2x + x2 = 0 + 4x + -4x
-16 + 2x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-16 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 2x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 2x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 2x + x2 = 0 + 16
2x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
2x + x2 = 16

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 = 16 + 1

Reorder the terms:
1 + 2x + x2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + 2x + x2 = 17

Factor a perfect square on the left side:
(x + 1)(x + 1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 1) equal to 4.123105626 and -4.123105626.

Subproblem 1
x + 1 = 4.123105626

Simplifying
x + 1 = 4.123105626

Reorder the terms:
1 + x = 4.123105626

Solving
1 + x = 4.123105626

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 = 4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.123105626 + -1
x = 4.123105626 + -1

Combine like terms: 4.123105626 + -1 = 3.123105626
x = 3.123105626

Simplifying
x = 3.123105626

Subproblem 2
x + 1 = -4.123105626

Simplifying
x + 1 = -4.123105626

Reorder the terms:
1 + x = -4.123105626

Solving
1 + x = -4.123105626

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 = -4.123105626 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.123105626 + -1
x = -4.123105626 + -1

Combine like terms: -4.123105626 + -1 = -5.123105626
x = -5.123105626

Simplifying
x = -5.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.123105626, -5.123105626}