(8x+16)(-3x+12)=(6x-42)+8

Solution for (8x+16)(-3x+12)=(6x-42)+8 equation:

Simplifying
(8x + 16)(-3x + 12) = (6x + -42) + 8

Reorder the terms:
(16 + 8x)(-3x + 12) = (6x + -42) + 8

Reorder the terms:
(16 + 8x)(12 + -3x) = (6x + -42) + 8

Multiply (16 + 8x) * (12 + -3x)
(16(12 + -3x) + 8x * (12 + -3x)) = (6x + -42) + 8
((12 * 16 + -3x * 16) + 8x * (12 + -3x)) = (6x + -42) + 8
((192 + -48x) + 8x * (12 + -3x)) = (6x + -42) + 8
(192 + -48x + (12 * 8x + -3x * 8x)) = (6x + -42) + 8
(192 + -48x + (96x + -24x2)) = (6x + -42) + 8

Combine like terms: -48x + 96x = 48x
(192 + 48x + -24x2) = (6x + -42) + 8

Reorder the terms:
192 + 48x + -24x2 = (-42 + 6x) + 8

Remove parenthesis around (-42 + 6x)
192 + 48x + -24x2 = -42 + 6x + 8

Reorder the terms:
192 + 48x + -24x2 = -42 + 8 + 6x

Combine like terms: -42 + 8 = -34
192 + 48x + -24x2 = -34 + 6x

Solving
192 + 48x + -24x2 = -34 + 6x

Solving for variable 'x'.

Reorder the terms:
192 + 34 + 48x + -6x + -24x2 = -34 + 6x + 34 + -6x

Combine like terms: 192 + 34 = 226
226 + 48x + -6x + -24x2 = -34 + 6x + 34 + -6x

Combine like terms: 48x + -6x = 42x
226 + 42x + -24x2 = -34 + 6x + 34 + -6x

Reorder the terms:
226 + 42x + -24x2 = -34 + 34 + 6x + -6x

Combine like terms: -34 + 34 = 0
226 + 42x + -24x2 = 0 + 6x + -6x
226 + 42x + -24x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
226 + 42x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(113 + 21x + -12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(113 + 21x + -12x2)' equal to zero and attempt to solve:

Simplifying
113 + 21x + -12x2 = 0

Solving
113 + 21x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-9.416666667 + -1.75x + x2 = 0

Move the constant term to the right:

Add '9.416666667' to each side of the equation.
-9.416666667 + -1.75x + 9.416666667 + x2 = 0 + 9.416666667

Reorder the terms:
-9.416666667 + 9.416666667 + -1.75x + x2 = 0 + 9.416666667

Combine like terms: -9.416666667 + 9.416666667 = 0.000000000
0.000000000 + -1.75x + x2 = 0 + 9.416666667
-1.75x + x2 = 0 + 9.416666667

Combine like terms: 0 + 9.416666667 = 9.416666667
-1.75x + x2 = 9.416666667

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 9.416666667 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 9.416666667 + 0.765625

Combine like terms: 9.416666667 + 0.765625 = 10.182291667
0.765625 + -1.75x + x2 = 10.182291667

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 10.182291667

Calculate the square root of the right side: 3.190970333

Break this problem into two subproblems by setting 
(x + -0.875) equal to 3.190970333 and -3.190970333.

Subproblem 1
x + -0.875 = 3.190970333

Simplifying
x + -0.875 = 3.190970333

Reorder the terms:
-0.875 + x = 3.190970333

Solving
-0.875 + x = 3.190970333

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 3.190970333 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 3.190970333 + 0.875
x = 3.190970333 + 0.875

Combine like terms: 3.190970333 + 0.875 = 4.065970333
x = 4.065970333

Simplifying
x = 4.065970333

Subproblem 2
x + -0.875 = -3.190970333

Simplifying
x + -0.875 = -3.190970333

Reorder the terms:
-0.875 + x = -3.190970333

Solving
-0.875 + x = -3.190970333

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -3.190970333 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -3.190970333 + 0.875
x = -3.190970333 + 0.875

Combine like terms: -3.190970333 + 0.875 = -2.315970333
x = -2.315970333

Simplifying
x = -2.315970333

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.065970333, -2.315970333}
Solution
x = {4.065970333, -2.315970333}