-4(3x+4)-(2x+6)x=4

Solution for -4(3x+4)-(2x+6)x=4 equation:

Simplifying
-4(3x + 4) + -1(2x + 6) * x = 4

Reorder the terms:
-4(4 + 3x) + -1(2x + 6) * x = 4
(4 * -4 + 3x * -4) + -1(2x + 6) * x = 4
(-16 + -12x) + -1(2x + 6) * x = 4

Reorder the terms:
-16 + -12x + -1(6 + 2x) * x = 4

Reorder the terms for easier multiplication:
-16 + -12x + -1x(6 + 2x) = 4
-16 + -12x + (6 * -1x + 2x * -1x) = 4
-16 + -12x + (-6x + -2x2) = 4

Combine like terms: -12x + -6x = -18x
-16 + -18x + -2x2 = 4

Solving
-16 + -18x + -2x2 = 4

Solving for variable 'x'.

Reorder the terms:
-16 + -4 + -18x + -2x2 = 4 + -4

Combine like terms: -16 + -4 = -20
-20 + -18x + -2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-20 + -18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(10 + 9x + x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(10 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 9x + x2 = 0

Solving
10 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 9x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 9x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x + x2 = 0 + -10
9x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
9x + x2 = -10

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -10 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + 9x + x2 = 10.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + 4.5 = 3.201562119

Simplifying
x + 4.5 = 3.201562119

Reorder the terms:
4.5 + x = 3.201562119

Solving
4.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.201562119 + -4.5
x = 3.201562119 + -4.5

Combine like terms: 3.201562119 + -4.5 = -1.298437881
x = -1.298437881

Simplifying
x = -1.298437881

Subproblem 2
x + 4.5 = -3.201562119

Simplifying
x + 4.5 = -3.201562119

Reorder the terms:
4.5 + x = -3.201562119

Solving
4.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.201562119 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.201562119 + -4.5
x = -3.201562119 + -4.5

Combine like terms: -3.201562119 + -4.5 = -7.701562119
x = -7.701562119

Simplifying
x = -7.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.298437881, -7.701562119}
Solution
x = {-1.298437881, -7.701562119}