6x+4+5x(x+6)=12

Solution for 6x+4+5x(x+6)=12 equation:

Simplifying
6x + 4 + 5x(x + 6) = 12

Reorder the terms:
6x + 4 + 5x(6 + x) = 12
6x + 4 + (6 * 5x + x * 5x) = 12
6x + 4 + (30x + 5x2) = 12

Reorder the terms:
4 + 6x + 30x + 5x2 = 12

Combine like terms: 6x + 30x = 36x
4 + 36x + 5x2 = 12

Solving
4 + 36x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
4 + -12 + 36x + 5x2 = 12 + -12

Combine like terms: 4 + -12 = -8
-8 + 36x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-8 + 36x + 5x2 = 0

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

Divide each side by '5'.
-1.6 + 7.2x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 7.2x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 7.2x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 7.2x + x2 = 0 + 1.6
7.2x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
7.2x + x2 = 1.6

The x term is 7.2x.  Take half its coefficient (3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
7.2x + 12.96 + x2 = 1.6 + 12.96

Reorder the terms:
12.96 + 7.2x + x2 = 1.6 + 12.96

Combine like terms: 1.6 + 12.96 = 14.56
12.96 + 7.2x + x2 = 14.56

Factor a perfect square on the left side:
(x + 3.6)(x + 3.6) = 14.56

Calculate the square root of the right side: 3.815756806

Break this problem into two subproblems by setting 
(x + 3.6) equal to 3.815756806 and -3.815756806.

Subproblem 1
x + 3.6 = 3.815756806

Simplifying
x + 3.6 = 3.815756806

Reorder the terms:
3.6 + x = 3.815756806

Solving
3.6 + x = 3.815756806

Solving for variable 'x'.

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

Add '-3.6' to each side of the equation.
3.6 + -3.6 + x = 3.815756806 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + x = 3.815756806 + -3.6
x = 3.815756806 + -3.6

Combine like terms: 3.815756806 + -3.6 = 0.215756806
x = 0.215756806

Simplifying
x = 0.215756806

Subproblem 2
x + 3.6 = -3.815756806

Simplifying
x + 3.6 = -3.815756806

Reorder the terms:
3.6 + x = -3.815756806

Solving
3.6 + x = -3.815756806

Solving for variable 'x'.

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

Add '-3.6' to each side of the equation.
3.6 + -3.6 + x = -3.815756806 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + x = -3.815756806 + -3.6
x = -3.815756806 + -3.6

Combine like terms: -3.815756806 + -3.6 = -7.415756806
x = -7.415756806

Simplifying
x = -7.415756806

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.215756806, -7.415756806}