3x(2x+6)=17+(8x+1)

Solution for 3x(2x+6)=17+(8x+1) equation:

Simplifying
3x(2x + 6) = 17 + (8x + 1)

Reorder the terms:
3x(6 + 2x) = 17 + (8x + 1)
(6 * 3x + 2x * 3x) = 17 + (8x + 1)
(18x + 6x2) = 17 + (8x + 1)

Reorder the terms:
18x + 6x2 = 17 + (1 + 8x)

Remove parenthesis around (1 + 8x)
18x + 6x2 = 17 + 1 + 8x

Combine like terms: 17 + 1 = 18
18x + 6x2 = 18 + 8x

Solving
18x + 6x2 = 18 + 8x

Solving for variable 'x'.

Reorder the terms:
-18 + 18x + -8x + 6x2 = 18 + 8x + -18 + -8x

Combine like terms: 18x + -8x = 10x
-18 + 10x + 6x2 = 18 + 8x + -18 + -8x

Reorder the terms:
-18 + 10x + 6x2 = 18 + -18 + 8x + -8x

Combine like terms: 18 + -18 = 0
-18 + 10x + 6x2 = 0 + 8x + -8x
-18 + 10x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-18 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-9 + 5x + 3x2 = 0

Solving
-9 + 5x + 3x2 = 0

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

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

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.666666667x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.666666667x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.666666667x + x2 = 0 + 3
1.666666667x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.666666667x + x2 = 3

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 = 3 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 3 + 0.6944444447

Combine like terms: 3 + 0.6944444447 = 3.6944444447
0.6944444447 + 1.666666667x + x2 = 3.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 3.6944444447

Calculate the square root of the right side: 1.922093766

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.922093766 and -1.922093766.

Subproblem 1
x + 0.8333333335 = 1.922093766

Simplifying
x + 0.8333333335 = 1.922093766

Reorder the terms:
0.8333333335 + x = 1.922093766

Solving
0.8333333335 + x = 1.922093766

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 = 1.922093766 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.922093766 + -0.8333333335
x = 1.922093766 + -0.8333333335

Combine like terms: 1.922093766 + -0.8333333335 = 1.0887604325
x = 1.0887604325

Simplifying
x = 1.0887604325

Subproblem 2
x + 0.8333333335 = -1.922093766

Simplifying
x + 0.8333333335 = -1.922093766

Reorder the terms:
0.8333333335 + x = -1.922093766

Solving
0.8333333335 + x = -1.922093766

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 = -1.922093766 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.922093766 + -0.8333333335
x = -1.922093766 + -0.8333333335

Combine like terms: -1.922093766 + -0.8333333335 = -2.7554270995
x = -2.7554270995

Simplifying
x = -2.7554270995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0887604325, -2.7554270995}
Solution
x = {1.0887604325, -2.7554270995}