-5x(3x+14)=6-(3x+4)

Solution for -5x(3x+14)=6-(3x+4) equation:

Simplifying
-5x(3x + 14) = 6 + -1(3x + 4)

Reorder the terms:
-5x(14 + 3x) = 6 + -1(3x + 4)
(14 * -5x + 3x * -5x) = 6 + -1(3x + 4)
(-70x + -15x2) = 6 + -1(3x + 4)

Reorder the terms:
-70x + -15x2 = 6 + -1(4 + 3x)
-70x + -15x2 = 6 + (4 * -1 + 3x * -1)
-70x + -15x2 = 6 + (-4 + -3x)

Combine like terms: 6 + -4 = 2
-70x + -15x2 = 2 + -3x

Solving
-70x + -15x2 = 2 + -3x

Solving for variable 'x'.

Reorder the terms:
-2 + -70x + 3x + -15x2 = 2 + -3x + -2 + 3x

Combine like terms: -70x + 3x = -67x
-2 + -67x + -15x2 = 2 + -3x + -2 + 3x

Reorder the terms:
-2 + -67x + -15x2 = 2 + -2 + -3x + 3x

Combine like terms: 2 + -2 = 0
-2 + -67x + -15x2 = 0 + -3x + 3x
-2 + -67x + -15x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-2 + -67x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 67x + 15x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 67x + 15x2)' equal to zero and attempt to solve:

Simplifying
2 + 67x + 15x2 = 0

Solving
2 + 67x + 15x2 = 0

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

Divide each side by '15'.
0.1333333333 + 4.466666667x + x2 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + 4.466666667x + -0.1333333333 + x2 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + 4.466666667x + x2 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + 4.466666667x + x2 = 0 + -0.1333333333
4.466666667x + x2 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
4.466666667x + x2 = -0.1333333333

The x term is 4.466666667x.  Take half its coefficient (2.233333334).
Square it (4.987777781) and add it to both sides.

Add '4.987777781' to each side of the equation.
4.466666667x + 4.987777781 + x2 = -0.1333333333 + 4.987777781

Reorder the terms:
4.987777781 + 4.466666667x + x2 = -0.1333333333 + 4.987777781

Combine like terms: -0.1333333333 + 4.987777781 = 4.8544444477
4.987777781 + 4.466666667x + x2 = 4.8544444477

Factor a perfect square on the left side:
(x + 2.233333334)(x + 2.233333334) = 4.8544444477

Calculate the square root of the right side: 2.203280383

Break this problem into two subproblems by setting 
(x + 2.233333334) equal to 2.203280383 and -2.203280383.

Subproblem 1
x + 2.233333334 = 2.203280383

Simplifying
x + 2.233333334 = 2.203280383

Reorder the terms:
2.233333334 + x = 2.203280383

Solving
2.233333334 + x = 2.203280383

Solving for variable 'x'.

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

Add '-2.233333334' to each side of the equation.
2.233333334 + -2.233333334 + x = 2.203280383 + -2.233333334

Combine like terms: 2.233333334 + -2.233333334 = 0.000000000
0.000000000 + x = 2.203280383 + -2.233333334
x = 2.203280383 + -2.233333334

Combine like terms: 2.203280383 + -2.233333334 = -0.030052951
x = -0.030052951

Simplifying
x = -0.030052951

Subproblem 2
x + 2.233333334 = -2.203280383

Simplifying
x + 2.233333334 = -2.203280383

Reorder the terms:
2.233333334 + x = -2.203280383

Solving
2.233333334 + x = -2.203280383

Solving for variable 'x'.

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

Add '-2.233333334' to each side of the equation.
2.233333334 + -2.233333334 + x = -2.203280383 + -2.233333334

Combine like terms: 2.233333334 + -2.233333334 = 0.000000000
0.000000000 + x = -2.203280383 + -2.233333334
x = -2.203280383 + -2.233333334

Combine like terms: -2.203280383 + -2.233333334 = -4.436613717
x = -4.436613717

Simplifying
x = -4.436613717

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.030052951, -4.436613717}
Solution
x = {-0.030052951, -4.436613717}