(6x+2)(3x-8)=x(4x+17)

Solution for (6x+2)(3x-8)=x(4x+17) equation:

Simplifying
(6x + 2)(3x + -8) = x(4x + 17)

Reorder the terms:
(2 + 6x)(3x + -8) = x(4x + 17)

Reorder the terms:
(2 + 6x)(-8 + 3x) = x(4x + 17)

Multiply (2 + 6x) * (-8 + 3x)
(2(-8 + 3x) + 6x * (-8 + 3x)) = x(4x + 17)
((-8 * 2 + 3x * 2) + 6x * (-8 + 3x)) = x(4x + 17)
((-16 + 6x) + 6x * (-8 + 3x)) = x(4x + 17)
(-16 + 6x + (-8 * 6x + 3x * 6x)) = x(4x + 17)
(-16 + 6x + (-48x + 18x2)) = x(4x + 17)

Combine like terms: 6x + -48x = -42x
(-16 + -42x + 18x2) = x(4x + 17)

Reorder the terms:
-16 + -42x + 18x2 = x(17 + 4x)
-16 + -42x + 18x2 = (17 * x + 4x * x)
-16 + -42x + 18x2 = (17x + 4x2)

Solving
-16 + -42x + 18x2 = 17x + 4x2

Solving for variable 'x'.

Reorder the terms:
-16 + -42x + -17x + 18x2 + -4x2 = 17x + 4x2 + -17x + -4x2

Combine like terms: -42x + -17x = -59x
-16 + -59x + 18x2 + -4x2 = 17x + 4x2 + -17x + -4x2

Combine like terms: 18x2 + -4x2 = 14x2
-16 + -59x + 14x2 = 17x + 4x2 + -17x + -4x2

Reorder the terms:
-16 + -59x + 14x2 = 17x + -17x + 4x2 + -4x2

Combine like terms: 17x + -17x = 0
-16 + -59x + 14x2 = 0 + 4x2 + -4x2
-16 + -59x + 14x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + -59x + 14x2 = 0

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

Divide each side by '14'.
-1.142857143 + -4.214285714x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -4.214285714x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -4.214285714x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -4.214285714x + x2 = 0 + 1.142857143
-4.214285714x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-4.214285714x + x2 = 1.142857143

The x term is -4.214285714x.  Take half its coefficient (-2.107142857).
Square it (4.440051020) and add it to both sides.

Add '4.440051020' to each side of the equation.
-4.214285714x + 4.440051020 + x2 = 1.142857143 + 4.440051020

Reorder the terms:
4.440051020 + -4.214285714x + x2 = 1.142857143 + 4.440051020

Combine like terms: 1.142857143 + 4.440051020 = 5.582908163
4.440051020 + -4.214285714x + x2 = 5.582908163

Factor a perfect square on the left side:
(x + -2.107142857)(x + -2.107142857) = 5.582908163

Calculate the square root of the right side: 2.362817844

Break this problem into two subproblems by setting 
(x + -2.107142857) equal to 2.362817844 and -2.362817844.

Subproblem 1
x + -2.107142857 = 2.362817844

Simplifying
x + -2.107142857 = 2.362817844

Reorder the terms:
-2.107142857 + x = 2.362817844

Solving
-2.107142857 + x = 2.362817844

Solving for variable 'x'.

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

Add '2.107142857' to each side of the equation.
-2.107142857 + 2.107142857 + x = 2.362817844 + 2.107142857

Combine like terms: -2.107142857 + 2.107142857 = 0.000000000
0.000000000 + x = 2.362817844 + 2.107142857
x = 2.362817844 + 2.107142857

Combine like terms: 2.362817844 + 2.107142857 = 4.469960701
x = 4.469960701

Simplifying
x = 4.469960701

Subproblem 2
x + -2.107142857 = -2.362817844

Simplifying
x + -2.107142857 = -2.362817844

Reorder the terms:
-2.107142857 + x = -2.362817844

Solving
-2.107142857 + x = -2.362817844

Solving for variable 'x'.

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

Add '2.107142857' to each side of the equation.
-2.107142857 + 2.107142857 + x = -2.362817844 + 2.107142857

Combine like terms: -2.107142857 + 2.107142857 = 0.000000000
0.000000000 + x = -2.362817844 + 2.107142857
x = -2.362817844 + 2.107142857

Combine like terms: -2.362817844 + 2.107142857 = -0.255674987
x = -0.255674987

Simplifying
x = -0.255674987

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.469960701, -0.255674987}