-6x(8-4x)=7+(x-3)

Solution for -6x(8-4x)=7+(x-3) equation:

Simplifying
-6x(8 + -4x) = 7 + (x + -3)
(8 * -6x + -4x * -6x) = 7 + (x + -3)
(-48x + 24x2) = 7 + (x + -3)

Reorder the terms:
-48x + 24x2 = 7 + (-3 + x)

Remove parenthesis around (-3 + x)
-48x + 24x2 = 7 + -3 + x

Combine like terms: 7 + -3 = 4
-48x + 24x2 = 4 + x

Solving
-48x + 24x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-4 + -48x + -1x + 24x2 = 4 + x + -4 + -1x

Combine like terms: -48x + -1x = -49x
-4 + -49x + 24x2 = 4 + x + -4 + -1x

Reorder the terms:
-4 + -49x + 24x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-4 + -49x + 24x2 = 0 + x + -1x
-4 + -49x + 24x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + -49x + 24x2 = 0

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

Divide each side by '24'.
-0.1666666667 + -2.041666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -2.041666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -2.041666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -2.041666667x + x2 = 0 + 0.1666666667
-2.041666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-2.041666667x + x2 = 0.1666666667

The x term is -2.041666667x.  Take half its coefficient (-1.020833334).
Square it (1.042100696) and add it to both sides.

Add '1.042100696' to each side of the equation.
-2.041666667x + 1.042100696 + x2 = 0.1666666667 + 1.042100696

Reorder the terms:
1.042100696 + -2.041666667x + x2 = 0.1666666667 + 1.042100696

Combine like terms: 0.1666666667 + 1.042100696 = 1.2087673627
1.042100696 + -2.041666667x + x2 = 1.2087673627

Factor a perfect square on the left side:
(x + -1.020833334)(x + -1.020833334) = 1.2087673627

Calculate the square root of the right side: 1.099439568

Break this problem into two subproblems by setting 
(x + -1.020833334) equal to 1.099439568 and -1.099439568.

Subproblem 1
x + -1.020833334 = 1.099439568

Simplifying
x + -1.020833334 = 1.099439568

Reorder the terms:
-1.020833334 + x = 1.099439568

Solving
-1.020833334 + x = 1.099439568

Solving for variable 'x'.

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

Add '1.020833334' to each side of the equation.
-1.020833334 + 1.020833334 + x = 1.099439568 + 1.020833334

Combine like terms: -1.020833334 + 1.020833334 = 0.000000000
0.000000000 + x = 1.099439568 + 1.020833334
x = 1.099439568 + 1.020833334

Combine like terms: 1.099439568 + 1.020833334 = 2.120272902
x = 2.120272902

Simplifying
x = 2.120272902

Subproblem 2
x + -1.020833334 = -1.099439568

Simplifying
x + -1.020833334 = -1.099439568

Reorder the terms:
-1.020833334 + x = -1.099439568

Solving
-1.020833334 + x = -1.099439568

Solving for variable 'x'.

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

Add '1.020833334' to each side of the equation.
-1.020833334 + 1.020833334 + x = -1.099439568 + 1.020833334

Combine like terms: -1.020833334 + 1.020833334 = 0.000000000
0.000000000 + x = -1.099439568 + 1.020833334
x = -1.099439568 + 1.020833334

Combine like terms: -1.099439568 + 1.020833334 = -0.078606234
x = -0.078606234

Simplifying
x = -0.078606234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.120272902, -0.078606234}