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

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

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

Reorder the terms:
17(3 + 2x) = (x + -3)(x + 3)
(3 * 17 + 2x * 17) = (x + -3)(x + 3)
(51 + 34x) = (x + -3)(x + 3)

Reorder the terms:
51 + 34x = (-3 + x)(x + 3)

Reorder the terms:
51 + 34x = (-3 + x)(3 + x)

Multiply (-3 + x) * (3 + x)
51 + 34x = (-3(3 + x) + x(3 + x))
51 + 34x = ((3 * -3 + x * -3) + x(3 + x))
51 + 34x = ((-9 + -3x) + x(3 + x))
51 + 34x = (-9 + -3x + (3 * x + x * x))
51 + 34x = (-9 + -3x + (3x + x2))

Combine like terms: -3x + 3x = 0
51 + 34x = (-9 + 0 + x2)
51 + 34x = (-9 + x2)

Solving
51 + 34x = -9 + x2

Solving for variable 'x'.

Reorder the terms:
51 + 9 + 34x + -1x2 = -9 + x2 + 9 + -1x2

Combine like terms: 51 + 9 = 60
60 + 34x + -1x2 = -9 + x2 + 9 + -1x2

Reorder the terms:
60 + 34x + -1x2 = -9 + 9 + x2 + -1x2

Combine like terms: -9 + 9 = 0
60 + 34x + -1x2 = 0 + x2 + -1x2
60 + 34x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + 34x + -1x2 = 0

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

Divide each side by '-1'.
-60 + -34x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -34x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -34x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -34x + x2 = 0 + 60
-34x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-34x + x2 = 60

The x term is -34x.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x + 289 + x2 = 60 + 289

Reorder the terms:
289 + -34x + x2 = 60 + 289

Combine like terms: 60 + 289 = 349
289 + -34x + x2 = 349

Factor a perfect square on the left side:
(x + -17)(x + -17) = 349

Calculate the square root of the right side: 18.681541692

Break this problem into two subproblems by setting 
(x + -17) equal to 18.681541692 and -18.681541692.

Subproblem 1
x + -17 = 18.681541692

Simplifying
x + -17 = 18.681541692

Reorder the terms:
-17 + x = 18.681541692

Solving
-17 + x = 18.681541692

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = 18.681541692 + 17

Combine like terms: -17 + 17 = 0
0 + x = 18.681541692 + 17
x = 18.681541692 + 17

Combine like terms: 18.681541692 + 17 = 35.681541692
x = 35.681541692

Simplifying
x = 35.681541692

Subproblem 2
x + -17 = -18.681541692

Simplifying
x + -17 = -18.681541692

Reorder the terms:
-17 + x = -18.681541692

Solving
-17 + x = -18.681541692

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = -18.681541692 + 17

Combine like terms: -17 + 17 = 0
0 + x = -18.681541692 + 17
x = -18.681541692 + 17

Combine like terms: -18.681541692 + 17 = -1.681541692
x = -1.681541692

Simplifying
x = -1.681541692

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.681541692, -1.681541692}