-3x(x-8)=6

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

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

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

Solving
24x + -3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 24x + -3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 8x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-2 + 8x + -1x2 = 0

Solving
-2 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -8x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -8x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -8x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -8x + x2 = 0 + -2
-8x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-8x + x2 = -2

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -2 + 16

Reorder the terms:
16 + -8x + x2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + -8x + x2 = 14

Factor a perfect square on the left side:
(x + -4)(x + -4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -4) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + -4 = 3.741657387

Simplifying
x + -4 = 3.741657387

Reorder the terms:
-4 + x = 3.741657387

Solving
-4 + x = 3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.741657387 + 4
x = 3.741657387 + 4

Combine like terms: 3.741657387 + 4 = 7.741657387
x = 7.741657387

Simplifying
x = 7.741657387

Subproblem 2
x + -4 = -3.741657387

Simplifying
x + -4 = -3.741657387

Reorder the terms:
-4 + x = -3.741657387

Solving
-4 + x = -3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.741657387 + 4
x = -3.741657387 + 4

Combine like terms: -3.741657387 + 4 = 0.258342613
x = 0.258342613

Simplifying
x = 0.258342613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.741657387, 0.258342613}
Solution
x = {7.741657387, 0.258342613}