3x(x-1)-6-x-(x+8)=0

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Solution for 3x(x-1)-6-x-(x+8)=0 equation:


Simplifying
3x(x + -1) + -6 + -1x + -1(x + 8) = 0

Reorder the terms:
3x(-1 + x) + -6 + -1x + -1(x + 8) = 0
(-1 * 3x + x * 3x) + -6 + -1x + -1(x + 8) = 0
(-3x + 3x2) + -6 + -1x + -1(x + 8) = 0

Reorder the terms:
-3x + 3x2 + -6 + -1x + -1(8 + x) = 0
-3x + 3x2 + -6 + -1x + (8 * -1 + x * -1) = 0
-3x + 3x2 + -6 + -1x + (-8 + -1x) = 0

Reorder the terms:
-6 + -8 + -3x + -1x + -1x + 3x2 = 0

Combine like terms: -6 + -8 = -14
-14 + -3x + -1x + -1x + 3x2 = 0

Combine like terms: -3x + -1x = -4x
-14 + -4x + -1x + 3x2 = 0

Combine like terms: -4x + -1x = -5x
-14 + -5x + 3x2 = 0

Solving
-14 + -5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-4.666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -1.666666667x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -1.666666667x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 4.666666667
-1.666666667x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-1.666666667x + x2 = 4.666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 4.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 4.666666667 + 0.6944444447

Combine like terms: 4.666666667 + 0.6944444447 = 5.3611111117
0.6944444447 + -1.666666667x + x2 = 5.3611111117

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 5.3611111117

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 2.315407332 and -2.315407332.

Subproblem 1

x + -0.8333333335 = 2.315407332 Simplifying x + -0.8333333335 = 2.315407332 Reorder the terms: -0.8333333335 + x = 2.315407332 Solving -0.8333333335 + x = 2.315407332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.315407332 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.315407332 + 0.8333333335 x = 2.315407332 + 0.8333333335 Combine like terms: 2.315407332 + 0.8333333335 = 3.1487406655 x = 3.1487406655 Simplifying x = 3.1487406655

Subproblem 2

x + -0.8333333335 = -2.315407332 Simplifying x + -0.8333333335 = -2.315407332 Reorder the terms: -0.8333333335 + x = -2.315407332 Solving -0.8333333335 + x = -2.315407332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.315407332 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.315407332 + 0.8333333335 x = -2.315407332 + 0.8333333335 Combine like terms: -2.315407332 + 0.8333333335 = -1.4820739985 x = -1.4820739985 Simplifying x = -1.4820739985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.1487406655, -1.4820739985}

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