(2x+17)(1-3x)=18

Solution for (2x+17)(1-3x)=18 equation:

Simplifying
(2x + 17)(1 + -3x) = 18

Reorder the terms:
(17 + 2x)(1 + -3x) = 18

Multiply (17 + 2x) * (1 + -3x)
(17(1 + -3x) + 2x * (1 + -3x)) = 18
((1 * 17 + -3x * 17) + 2x * (1 + -3x)) = 18
((17 + -51x) + 2x * (1 + -3x)) = 18
(17 + -51x + (1 * 2x + -3x * 2x)) = 18
(17 + -51x + (2x + -6x2)) = 18

Combine like terms: -51x + 2x = -49x
(17 + -49x + -6x2) = 18

Solving
17 + -49x + -6x2 = 18

Solving for variable 'x'.

Reorder the terms:
17 + -18 + -49x + -6x2 = 18 + -18

Combine like terms: 17 + -18 = -1
-1 + -49x + -6x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-1 + -49x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 49x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 49x + 6x2)' equal to zero and attempt to solve:

Simplifying
1 + 49x + 6x2 = 0

Solving
1 + 49x + 6x2 = 0

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

Divide each side by '6'.
0.1666666667 + 8.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 8.166666667x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 8.166666667x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 8.166666667x + x2 = 0 + -0.1666666667
8.166666667x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
8.166666667x + x2 = -0.1666666667

The x term is 8.166666667x.  Take half its coefficient (4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
8.166666667x + 16.67361112 + x2 = -0.1666666667 + 16.67361112

Reorder the terms:
16.67361112 + 8.166666667x + x2 = -0.1666666667 + 16.67361112

Combine like terms: -0.1666666667 + 16.67361112 = 16.5069444533
16.67361112 + 8.166666667x + x2 = 16.5069444533

Factor a perfect square on the left side:
(x + 4.083333334)(x + 4.083333334) = 16.5069444533

Calculate the square root of the right side: 4.062873916

Break this problem into two subproblems by setting 
(x + 4.083333334) equal to 4.062873916 and -4.062873916.

Subproblem 1
x + 4.083333334 = 4.062873916

Simplifying
x + 4.083333334 = 4.062873916

Reorder the terms:
4.083333334 + x = 4.062873916

Solving
4.083333334 + x = 4.062873916

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = 4.062873916 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = 4.062873916 + -4.083333334
x = 4.062873916 + -4.083333334

Combine like terms: 4.062873916 + -4.083333334 = -0.020459418
x = -0.020459418

Simplifying
x = -0.020459418

Subproblem 2
x + 4.083333334 = -4.062873916

Simplifying
x + 4.083333334 = -4.062873916

Reorder the terms:
4.083333334 + x = -4.062873916

Solving
4.083333334 + x = -4.062873916

Solving for variable 'x'.

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

Add '-4.083333334' to each side of the equation.
4.083333334 + -4.083333334 + x = -4.062873916 + -4.083333334

Combine like terms: 4.083333334 + -4.083333334 = 0.000000000
0.000000000 + x = -4.062873916 + -4.083333334
x = -4.062873916 + -4.083333334

Combine like terms: -4.062873916 + -4.083333334 = -8.14620725
x = -8.14620725

Simplifying
x = -8.14620725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.020459418, -8.14620725}
Solution
x = {-0.020459418, -8.14620725}