-83=-7(3x-3)8x

Solution for -83=-7(3x-3)8x equation:

Simplifying
-83 = -7(3x + -3) * 8x

Reorder the terms:
-83 = -7(-3 + 3x) * 8x

Reorder the terms for easier multiplication:
-83 = -7 * 8x(-3 + 3x)

Multiply -7 * 8
-83 = -56x(-3 + 3x)
-83 = (-3 * -56x + 3x * -56x)
-83 = (168x + -168x2)

Solving
-83 = 168x + -168x2

Solving for variable 'x'.

Reorder the terms:
-83 + -168x + 168x2 = 168x + -168x + -168x2 + 168x2

Combine like terms: 168x + -168x = 0
-83 + -168x + 168x2 = 0 + -168x2 + 168x2
-83 + -168x + 168x2 = -168x2 + 168x2

Combine like terms: -168x2 + 168x2 = 0
-83 + -168x + 168x2 = 0

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

Divide each side by '168'.
-0.494047619 + -1x + x2 = 0

Move the constant term to the right:

Add '0.494047619' to each side of the equation.
-0.494047619 + -1x + 0.494047619 + x2 = 0 + 0.494047619

Reorder the terms:
-0.494047619 + 0.494047619 + -1x + x2 = 0 + 0.494047619

Combine like terms: -0.494047619 + 0.494047619 = 0.000000000
0.000000000 + -1x + x2 = 0 + 0.494047619
-1x + x2 = 0 + 0.494047619

Combine like terms: 0 + 0.494047619 = 0.494047619
-1x + x2 = 0.494047619

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.494047619 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.494047619 + 0.25

Combine like terms: 0.494047619 + 0.25 = 0.744047619
0.25 + -1x + x2 = 0.744047619

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.744047619

Calculate the square root of the right side: 0.862581949

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.862581949 and -0.862581949.

Subproblem 1
x + -0.5 = 0.862581949

Simplifying
x + -0.5 = 0.862581949

Reorder the terms:
-0.5 + x = 0.862581949

Solving
-0.5 + x = 0.862581949

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.862581949 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.862581949 + 0.5
x = 0.862581949 + 0.5

Combine like terms: 0.862581949 + 0.5 = 1.362581949
x = 1.362581949

Simplifying
x = 1.362581949

Subproblem 2
x + -0.5 = -0.862581949

Simplifying
x + -0.5 = -0.862581949

Reorder the terms:
-0.5 + x = -0.862581949

Solving
-0.5 + x = -0.862581949

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.862581949 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.862581949 + 0.5
x = -0.862581949 + 0.5

Combine like terms: -0.862581949 + 0.5 = -0.362581949
x = -0.362581949

Simplifying
x = -0.362581949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.362581949, -0.362581949}