-14=6x-8x(x+3)

Solution for -14=6x-8x(x+3) equation:

Simplifying
-14 = 6x + -8x(x + 3)

Reorder the terms:
-14 = 6x + -8x(3 + x)
-14 = 6x + (3 * -8x + x * -8x)
-14 = 6x + (-24x + -8x2)

Combine like terms: 6x + -24x = -18x
-14 = -18x + -8x2

Solving
-14 = -18x + -8x2

Solving for variable 'x'.

Reorder the terms:
-14 + 18x + 8x2 = -18x + 18x + -8x2 + 8x2

Combine like terms: -18x + 18x = 0
-14 + 18x + 8x2 = 0 + -8x2 + 8x2
-14 + 18x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-14 + 18x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 9x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 9x + 4x2)' equal to zero and attempt to solve:

Simplifying
-7 + 9x + 4x2 = 0

Solving
-7 + 9x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + 2.25x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 2.25x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 2.25x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 2.25x + x2 = 0 + 1.75
2.25x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
2.25x + x2 = 1.75

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 1.75 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 1.75 + 1.265625

Combine like terms: 1.75 + 1.265625 = 3.015625
1.265625 + 2.25x + x2 = 3.015625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.736555499 and -1.736555499.

Subproblem 1
x + 1.125 = 1.736555499

Simplifying
x + 1.125 = 1.736555499

Reorder the terms:
1.125 + x = 1.736555499

Solving
1.125 + x = 1.736555499

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.736555499 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.736555499 + -1.125
x = 1.736555499 + -1.125

Combine like terms: 1.736555499 + -1.125 = 0.611555499
x = 0.611555499

Simplifying
x = 0.611555499

Subproblem 2
x + 1.125 = -1.736555499

Simplifying
x + 1.125 = -1.736555499

Reorder the terms:
1.125 + x = -1.736555499

Solving
1.125 + x = -1.736555499

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.736555499 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.736555499 + -1.125
x = -1.736555499 + -1.125

Combine like terms: -1.736555499 + -1.125 = -2.861555499
x = -2.861555499

Simplifying
x = -2.861555499

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.611555499, -2.861555499}
Solution
x = {0.611555499, -2.861555499}