x=(3x+7)(-4x-6)

Solution for x=(3x+7)(-4x-6) equation:

Simplifying
x = (3x + 7)(-4x + -6)

Reorder the terms:
x = (7 + 3x)(-4x + -6)

Reorder the terms:
x = (7 + 3x)(-6 + -4x)

Multiply (7 + 3x) * (-6 + -4x)
x = (7(-6 + -4x) + 3x * (-6 + -4x))
x = ((-6 * 7 + -4x * 7) + 3x * (-6 + -4x))
x = ((-42 + -28x) + 3x * (-6 + -4x))
x = (-42 + -28x + (-6 * 3x + -4x * 3x))
x = (-42 + -28x + (-18x + -12x2))

Combine like terms: -28x + -18x = -46x
x = (-42 + -46x + -12x2)

Solving
x = -42 + -46x + -12x2

Solving for variable 'x'.

Reorder the terms:
42 + x + 46x + 12x2 = -42 + -46x + -12x2 + 42 + 46x + 12x2

Combine like terms: x + 46x = 47x
42 + 47x + 12x2 = -42 + -46x + -12x2 + 42 + 46x + 12x2

Reorder the terms:
42 + 47x + 12x2 = -42 + 42 + -46x + 46x + -12x2 + 12x2

Combine like terms: -42 + 42 = 0
42 + 47x + 12x2 = 0 + -46x + 46x + -12x2 + 12x2
42 + 47x + 12x2 = -46x + 46x + -12x2 + 12x2

Combine like terms: -46x + 46x = 0
42 + 47x + 12x2 = 0 + -12x2 + 12x2
42 + 47x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
42 + 47x + 12x2 = 0

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

Divide each side by '12'.
3.5 + 3.916666667x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 3.916666667x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 3.916666667x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 3.916666667x + x2 = 0 + -3.5
3.916666667x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
3.916666667x + x2 = -3.5

The x term is 3.916666667x.  Take half its coefficient (1.958333334).
Square it (3.835069447) and add it to both sides.

Add '3.835069447' to each side of the equation.
3.916666667x + 3.835069447 + x2 = -3.5 + 3.835069447

Reorder the terms:
3.835069447 + 3.916666667x + x2 = -3.5 + 3.835069447

Combine like terms: -3.5 + 3.835069447 = 0.335069447
3.835069447 + 3.916666667x + x2 = 0.335069447

Factor a perfect square on the left side:
(x + 1.958333334)(x + 1.958333334) = 0.335069447

Calculate the square root of the right side: 0.578851835

Break this problem into two subproblems by setting 
(x + 1.958333334) equal to 0.578851835 and -0.578851835.

Subproblem 1
x + 1.958333334 = 0.578851835

Simplifying
x + 1.958333334 = 0.578851835

Reorder the terms:
1.958333334 + x = 0.578851835

Solving
1.958333334 + x = 0.578851835

Solving for variable 'x'.

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

Add '-1.958333334' to each side of the equation.
1.958333334 + -1.958333334 + x = 0.578851835 + -1.958333334

Combine like terms: 1.958333334 + -1.958333334 = 0.000000000
0.000000000 + x = 0.578851835 + -1.958333334
x = 0.578851835 + -1.958333334

Combine like terms: 0.578851835 + -1.958333334 = -1.379481499
x = -1.379481499

Simplifying
x = -1.379481499

Subproblem 2
x + 1.958333334 = -0.578851835

Simplifying
x + 1.958333334 = -0.578851835

Reorder the terms:
1.958333334 + x = -0.578851835

Solving
1.958333334 + x = -0.578851835

Solving for variable 'x'.

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

Add '-1.958333334' to each side of the equation.
1.958333334 + -1.958333334 + x = -0.578851835 + -1.958333334

Combine like terms: 1.958333334 + -1.958333334 = 0.000000000
0.000000000 + x = -0.578851835 + -1.958333334
x = -0.578851835 + -1.958333334

Combine like terms: -0.578851835 + -1.958333334 = -2.537185169
x = -2.537185169

Simplifying
x = -2.537185169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.379481499, -2.537185169}