-6x(7+6x)=-42

Solution for -6x(7+6x)=-42 equation:

Simplifying
-6x(7 + 6x) = -42
(7 * -6x + 6x * -6x) = -42
(-42x + -36x2) = -42

Solving
-42x + -36x2 = -42

Solving for variable 'x'.

Reorder the terms:
42 + -42x + -36x2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + -42x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + -7x + -6x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + -7x + -6x2)' equal to zero and attempt to solve:

Simplifying
7 + -7x + -6x2 = 0

Solving
7 + -7x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.166666667 + 1.166666667x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 1.166666667x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 1.166666667x + x2 = 0 + 1.166666667
1.166666667x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
1.166666667x + x2 = 1.166666667

The x term is 1.166666667x.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667x + 0.3402777780 + x2 = 1.166666667 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667x + x2 = 1.166666667 + 0.3402777780

Combine like terms: 1.166666667 + 0.3402777780 = 1.506944445
0.3402777780 + 1.166666667x + x2 = 1.506944445

Factor a perfect square on the left side:
(x + 0.5833333335)(x + 0.5833333335) = 1.506944445

Calculate the square root of the right side: 1.227576655

Break this problem into two subproblems by setting 
(x + 0.5833333335) equal to 1.227576655 and -1.227576655.

Subproblem 1
x + 0.5833333335 = 1.227576655

Simplifying
x + 0.5833333335 = 1.227576655

Reorder the terms:
0.5833333335 + x = 1.227576655

Solving
0.5833333335 + x = 1.227576655

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = 1.227576655 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = 1.227576655 + -0.5833333335
x = 1.227576655 + -0.5833333335

Combine like terms: 1.227576655 + -0.5833333335 = 0.6442433215
x = 0.6442433215

Simplifying
x = 0.6442433215

Subproblem 2
x + 0.5833333335 = -1.227576655

Simplifying
x + 0.5833333335 = -1.227576655

Reorder the terms:
0.5833333335 + x = -1.227576655

Solving
0.5833333335 + x = -1.227576655

Solving for variable 'x'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + x = -1.227576655 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + x = -1.227576655 + -0.5833333335
x = -1.227576655 + -0.5833333335

Combine like terms: -1.227576655 + -0.5833333335 = -1.8109099885
x = -1.8109099885

Simplifying
x = -1.8109099885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6442433215, -1.8109099885}
Solution
x = {0.6442433215, -1.8109099885}