7x(-6-2x)=3

Solution for 7x(-6-2x)=3 equation:

Simplifying
7x(-6 + -2x) = 3
(-6 * 7x + -2x * 7x) = 3
(-42x + -14x2) = 3

Solving
-42x + -14x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -42x + -14x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -42x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 42x + 14x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 42x + 14x2)' equal to zero and attempt to solve:

Simplifying
3 + 42x + 14x2 = 0

Solving
3 + 42x + 14x2 = 0

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

Divide each side by '14'.
0.2142857143 + 3x + x2 = 0

Move the constant term to the right:

Add '-0.2142857143' to each side of the equation.
0.2142857143 + 3x + -0.2142857143 + x2 = 0 + -0.2142857143

Reorder the terms:
0.2142857143 + -0.2142857143 + 3x + x2 = 0 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + 3x + x2 = 0 + -0.2142857143
3x + x2 = 0 + -0.2142857143

Combine like terms: 0 + -0.2142857143 = -0.2142857143
3x + x2 = -0.2142857143

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -0.2142857143 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -0.2142857143 + 2.25

Combine like terms: -0.2142857143 + 2.25 = 2.0357142857
2.25 + 3x + x2 = 2.0357142857

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.0357142857

Calculate the square root of the right side: 1.426784597

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.426784597 and -1.426784597.

Subproblem 1
x + 1.5 = 1.426784597

Simplifying
x + 1.5 = 1.426784597

Reorder the terms:
1.5 + x = 1.426784597

Solving
1.5 + x = 1.426784597

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 1.426784597 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.426784597 + -1.5
x = 1.426784597 + -1.5

Combine like terms: 1.426784597 + -1.5 = -0.073215403
x = -0.073215403

Simplifying
x = -0.073215403

Subproblem 2
x + 1.5 = -1.426784597

Simplifying
x + 1.5 = -1.426784597

Reorder the terms:
1.5 + x = -1.426784597

Solving
1.5 + x = -1.426784597

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -1.426784597 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.426784597 + -1.5
x = -1.426784597 + -1.5

Combine like terms: -1.426784597 + -1.5 = -2.926784597
x = -2.926784597

Simplifying
x = -2.926784597

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.073215403, -2.926784597}
Solution
x = {-0.073215403, -2.926784597}