(3x+2)(-2x-8)=7

Solution for (3x+2)(-2x-8)=7 equation:

Simplifying
(3x + 2)(-2x + -8) = 7

Reorder the terms:
(2 + 3x)(-2x + -8) = 7

Reorder the terms:
(2 + 3x)(-8 + -2x) = 7

Multiply (2 + 3x) * (-8 + -2x)
(2(-8 + -2x) + 3x * (-8 + -2x)) = 7
((-8 * 2 + -2x * 2) + 3x * (-8 + -2x)) = 7
((-16 + -4x) + 3x * (-8 + -2x)) = 7
(-16 + -4x + (-8 * 3x + -2x * 3x)) = 7
(-16 + -4x + (-24x + -6x2)) = 7

Combine like terms: -4x + -24x = -28x
(-16 + -28x + -6x2) = 7

Solving
-16 + -28x + -6x2 = 7

Solving for variable 'x'.

Reorder the terms:
-16 + -7 + -28x + -6x2 = 7 + -7

Combine like terms: -16 + -7 = -23
-23 + -28x + -6x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-23 + -28x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(23 + 28x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(23 + 28x + 6x2)' equal to zero and attempt to solve:

Simplifying
23 + 28x + 6x2 = 0

Solving
23 + 28x + 6x2 = 0

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

Divide each side by '6'.
3.833333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.833333333' to each side of the equation.
3.833333333 + 4.666666667x + -3.833333333 + x2 = 0 + -3.833333333

Reorder the terms:
3.833333333 + -3.833333333 + 4.666666667x + x2 = 0 + -3.833333333

Combine like terms: 3.833333333 + -3.833333333 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + -3.833333333
4.666666667x + x2 = 0 + -3.833333333

Combine like terms: 0 + -3.833333333 = -3.833333333
4.666666667x + x2 = -3.833333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -3.833333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -3.833333333 + 5.444444448

Combine like terms: -3.833333333 + 5.444444448 = 1.611111115
5.444444448 + 4.666666667x + x2 = 1.611111115

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 1.611111115

Calculate the square root of the right side: 1.269295519

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 1.269295519 and -1.269295519.

Subproblem 1
x + 2.333333334 = 1.269295519

Simplifying
x + 2.333333334 = 1.269295519

Reorder the terms:
2.333333334 + x = 1.269295519

Solving
2.333333334 + x = 1.269295519

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 1.269295519 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 1.269295519 + -2.333333334
x = 1.269295519 + -2.333333334

Combine like terms: 1.269295519 + -2.333333334 = -1.064037815
x = -1.064037815

Simplifying
x = -1.064037815

Subproblem 2
x + 2.333333334 = -1.269295519

Simplifying
x + 2.333333334 = -1.269295519

Reorder the terms:
2.333333334 + x = -1.269295519

Solving
2.333333334 + x = -1.269295519

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -1.269295519 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -1.269295519 + -2.333333334
x = -1.269295519 + -2.333333334

Combine like terms: -1.269295519 + -2.333333334 = -3.602628853
x = -3.602628853

Simplifying
x = -3.602628853

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.064037815, -3.602628853}
Solution
x = {-1.064037815, -3.602628853}