-2x(3x+7)-4=2x+5

Solution for -2x(3x+7)-4=2x+5 equation:

Simplifying
-2x(3x + 7) + -4 = 2x + 5

Reorder the terms:
-2x(7 + 3x) + -4 = 2x + 5
(7 * -2x + 3x * -2x) + -4 = 2x + 5
(-14x + -6x2) + -4 = 2x + 5

Reorder the terms:
-4 + -14x + -6x2 = 2x + 5

Reorder the terms:
-4 + -14x + -6x2 = 5 + 2x

Solving
-4 + -14x + -6x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-4 + -5 + -14x + -2x + -6x2 = 5 + 2x + -5 + -2x

Combine like terms: -4 + -5 = -9
-9 + -14x + -2x + -6x2 = 5 + 2x + -5 + -2x

Combine like terms: -14x + -2x = -16x
-9 + -16x + -6x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-9 + -16x + -6x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-9 + -16x + -6x2 = 0 + 2x + -2x
-9 + -16x + -6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-9 + -16x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 16x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + 16x + 6x2)' equal to zero and attempt to solve:

Simplifying
9 + 16x + 6x2 = 0

Solving
9 + 16x + 6x2 = 0

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

Divide each side by '6'.
1.5 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 2.666666667x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2.666666667x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2.666666667x + x2 = 0 + -1.5
2.666666667x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2.666666667x + x2 = -1.5

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -1.5 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -1.5 + 1.777777780

Combine like terms: -1.5 + 1.777777780 = 0.27777778
1.777777780 + 2.666666667x + x2 = 0.27777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 0.27777778

Calculate the square root of the right side: 0.527046279

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 0.527046279 and -0.527046279.

Subproblem 1
x + 1.333333334 = 0.527046279

Simplifying
x + 1.333333334 = 0.527046279

Reorder the terms:
1.333333334 + x = 0.527046279

Solving
1.333333334 + x = 0.527046279

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 0.527046279 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 0.527046279 + -1.333333334
x = 0.527046279 + -1.333333334

Combine like terms: 0.527046279 + -1.333333334 = -0.806287055
x = -0.806287055

Simplifying
x = -0.806287055

Subproblem 2
x + 1.333333334 = -0.527046279

Simplifying
x + 1.333333334 = -0.527046279

Reorder the terms:
1.333333334 + x = -0.527046279

Solving
1.333333334 + x = -0.527046279

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -0.527046279 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -0.527046279 + -1.333333334
x = -0.527046279 + -1.333333334

Combine like terms: -0.527046279 + -1.333333334 = -1.860379613
x = -1.860379613

Simplifying
x = -1.860379613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.806287055, -1.860379613}
Solution
x = {-0.806287055, -1.860379613}