3x-3x(7x-16)=-168

Solution for 3x-3x(7x-16)=-168 equation:

Simplifying
3x + -3x(7x + -16) = -168

Reorder the terms:
3x + -3x(-16 + 7x) = -168
3x + (-16 * -3x + 7x * -3x) = -168
3x + (48x + -21x2) = -168

Combine like terms: 3x + 48x = 51x
51x + -21x2 = -168

Solving
51x + -21x2 = -168

Solving for variable 'x'.

Reorder the terms:
168 + 51x + -21x2 = -168 + 168

Combine like terms: -168 + 168 = 0
168 + 51x + -21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(56 + 17x + -7x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(56 + 17x + -7x2)' equal to zero and attempt to solve:

Simplifying
56 + 17x + -7x2 = 0

Solving
56 + 17x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-8 + -2.428571429x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -2.428571429x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -2.428571429x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -2.428571429x + x2 = 0 + 8
-2.428571429x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-2.428571429x + x2 = 8

The x term is -2.428571429x.  Take half its coefficient (-1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
-2.428571429x + 1.474489798 + x2 = 8 + 1.474489798

Reorder the terms:
1.474489798 + -2.428571429x + x2 = 8 + 1.474489798

Combine like terms: 8 + 1.474489798 = 9.474489798
1.474489798 + -2.428571429x + x2 = 9.474489798

Factor a perfect square on the left side:
(x + -1.214285715)(x + -1.214285715) = 9.474489798

Calculate the square root of the right side: 3.078065918

Break this problem into two subproblems by setting 
(x + -1.214285715) equal to 3.078065918 and -3.078065918.

Subproblem 1
x + -1.214285715 = 3.078065918

Simplifying
x + -1.214285715 = 3.078065918

Reorder the terms:
-1.214285715 + x = 3.078065918

Solving
-1.214285715 + x = 3.078065918

Solving for variable 'x'.

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

Add '1.214285715' to each side of the equation.
-1.214285715 + 1.214285715 + x = 3.078065918 + 1.214285715

Combine like terms: -1.214285715 + 1.214285715 = 0.000000000
0.000000000 + x = 3.078065918 + 1.214285715
x = 3.078065918 + 1.214285715

Combine like terms: 3.078065918 + 1.214285715 = 4.292351633
x = 4.292351633

Simplifying
x = 4.292351633

Subproblem 2
x + -1.214285715 = -3.078065918

Simplifying
x + -1.214285715 = -3.078065918

Reorder the terms:
-1.214285715 + x = -3.078065918

Solving
-1.214285715 + x = -3.078065918

Solving for variable 'x'.

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

Add '1.214285715' to each side of the equation.
-1.214285715 + 1.214285715 + x = -3.078065918 + 1.214285715

Combine like terms: -1.214285715 + 1.214285715 = 0.000000000
0.000000000 + x = -3.078065918 + 1.214285715
x = -3.078065918 + 1.214285715

Combine like terms: -3.078065918 + 1.214285715 = -1.863780203
x = -1.863780203

Simplifying
x = -1.863780203

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.292351633, -1.863780203}
Solution
x = {4.292351633, -1.863780203}