(7+6)6=(x+4)x

Solution for (7+6)6=(x+4)x equation:

Simplifying
(7 + 6) * 6 = (x + 4) * x

Combine like terms: 7 + 6 = 13
(13) * 6 = (x + 4) * x

Multiply 13 * 6
78 = (x + 4) * x

Reorder the terms:
78 = (4 + x) * x

Reorder the terms for easier multiplication:
78 = x(4 + x)
78 = (4 * x + x * x)
78 = (4x + x2)

Solving
78 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
78 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
78 + -4x + -1x2 = 0 + x2 + -1x2
78 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
78 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-78 + 4x + x2 = 0

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + 4x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + 4x + x2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + 4x + x2 = 0 + 78
4x + x2 = 0 + 78

Combine like terms: 0 + 78 = 78
4x + x2 = 78

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 78 + 4

Reorder the terms:
4 + 4x + x2 = 78 + 4

Combine like terms: 78 + 4 = 82
4 + 4x + x2 = 82

Factor a perfect square on the left side:
(x + 2)(x + 2) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 2) equal to 9.055385138 and -9.055385138.

Subproblem 1
x + 2 = 9.055385138

Simplifying
x + 2 = 9.055385138

Reorder the terms:
2 + x = 9.055385138

Solving
2 + x = 9.055385138

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + x = 9.055385138 + -2
x = 9.055385138 + -2

Combine like terms: 9.055385138 + -2 = 7.055385138
x = 7.055385138

Simplifying
x = 7.055385138

Subproblem 2
x + 2 = -9.055385138

Simplifying
x + 2 = -9.055385138

Reorder the terms:
2 + x = -9.055385138

Solving
2 + x = -9.055385138

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -9.055385138 + -2

Combine like terms: 2 + -2 = 0
0 + x = -9.055385138 + -2
x = -9.055385138 + -2

Combine like terms: -9.055385138 + -2 = -11.055385138
x = -11.055385138

Simplifying
x = -11.055385138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.055385138, -11.055385138}