(3x+5)(x+3)=(11x-9)(2x+1)

Solution for (3x+5)(x+3)=(11x-9)(2x+1) equation:

Simplifying
(3x + 5)(x + 3) = (11x + -9)(2x + 1)

Reorder the terms:
(5 + 3x)(x + 3) = (11x + -9)(2x + 1)

Reorder the terms:
(5 + 3x)(3 + x) = (11x + -9)(2x + 1)

Multiply (5 + 3x) * (3 + x)
(5(3 + x) + 3x * (3 + x)) = (11x + -9)(2x + 1)
((3 * 5 + x * 5) + 3x * (3 + x)) = (11x + -9)(2x + 1)
((15 + 5x) + 3x * (3 + x)) = (11x + -9)(2x + 1)
(15 + 5x + (3 * 3x + x * 3x)) = (11x + -9)(2x + 1)
(15 + 5x + (9x + 3x2)) = (11x + -9)(2x + 1)

Combine like terms: 5x + 9x = 14x
(15 + 14x + 3x2) = (11x + -9)(2x + 1)

Reorder the terms:
15 + 14x + 3x2 = (-9 + 11x)(2x + 1)

Reorder the terms:
15 + 14x + 3x2 = (-9 + 11x)(1 + 2x)

Multiply (-9 + 11x) * (1 + 2x)
15 + 14x + 3x2 = (-9(1 + 2x) + 11x * (1 + 2x))
15 + 14x + 3x2 = ((1 * -9 + 2x * -9) + 11x * (1 + 2x))
15 + 14x + 3x2 = ((-9 + -18x) + 11x * (1 + 2x))
15 + 14x + 3x2 = (-9 + -18x + (1 * 11x + 2x * 11x))
15 + 14x + 3x2 = (-9 + -18x + (11x + 22x2))

Combine like terms: -18x + 11x = -7x
15 + 14x + 3x2 = (-9 + -7x + 22x2)

Solving
15 + 14x + 3x2 = -9 + -7x + 22x2

Solving for variable 'x'.

Reorder the terms:
15 + 9 + 14x + 7x + 3x2 + -22x2 = -9 + -7x + 22x2 + 9 + 7x + -22x2

Combine like terms: 15 + 9 = 24
24 + 14x + 7x + 3x2 + -22x2 = -9 + -7x + 22x2 + 9 + 7x + -22x2

Combine like terms: 14x + 7x = 21x
24 + 21x + 3x2 + -22x2 = -9 + -7x + 22x2 + 9 + 7x + -22x2

Combine like terms: 3x2 + -22x2 = -19x2
24 + 21x + -19x2 = -9 + -7x + 22x2 + 9 + 7x + -22x2

Reorder the terms:
24 + 21x + -19x2 = -9 + 9 + -7x + 7x + 22x2 + -22x2

Combine like terms: -9 + 9 = 0
24 + 21x + -19x2 = 0 + -7x + 7x + 22x2 + -22x2
24 + 21x + -19x2 = -7x + 7x + 22x2 + -22x2

Combine like terms: -7x + 7x = 0
24 + 21x + -19x2 = 0 + 22x2 + -22x2
24 + 21x + -19x2 = 22x2 + -22x2

Combine like terms: 22x2 + -22x2 = 0
24 + 21x + -19x2 = 0

Begin completing the square.  Divide all terms by
-19 the coefficient of the squared term: 

Divide each side by '-19'.
-1.263157895 + -1.105263158x + x2 = 0

Move the constant term to the right:

Add '1.263157895' to each side of the equation.
-1.263157895 + -1.105263158x + 1.263157895 + x2 = 0 + 1.263157895

Reorder the terms:
-1.263157895 + 1.263157895 + -1.105263158x + x2 = 0 + 1.263157895

Combine like terms: -1.263157895 + 1.263157895 = 0.000000000
0.000000000 + -1.105263158x + x2 = 0 + 1.263157895
-1.105263158x + x2 = 0 + 1.263157895

Combine like terms: 0 + 1.263157895 = 1.263157895
-1.105263158x + x2 = 1.263157895

The x term is -1.105263158x.  Take half its coefficient (-0.552631579).
Square it (0.3054016621) and add it to both sides.

Add '0.3054016621' to each side of the equation.
-1.105263158x + 0.3054016621 + x2 = 1.263157895 + 0.3054016621

Reorder the terms:
0.3054016621 + -1.105263158x + x2 = 1.263157895 + 0.3054016621

Combine like terms: 1.263157895 + 0.3054016621 = 1.5685595571
0.3054016621 + -1.105263158x + x2 = 1.5685595571

Factor a perfect square on the left side:
(x + -0.552631579)(x + -0.552631579) = 1.5685595571

Calculate the square root of the right side: 1.252421477

Break this problem into two subproblems by setting 
(x + -0.552631579) equal to 1.252421477 and -1.252421477.

Subproblem 1
x + -0.552631579 = 1.252421477

Simplifying
x + -0.552631579 = 1.252421477

Reorder the terms:
-0.552631579 + x = 1.252421477

Solving
-0.552631579 + x = 1.252421477

Solving for variable 'x'.

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

Add '0.552631579' to each side of the equation.
-0.552631579 + 0.552631579 + x = 1.252421477 + 0.552631579

Combine like terms: -0.552631579 + 0.552631579 = 0.000000000
0.000000000 + x = 1.252421477 + 0.552631579
x = 1.252421477 + 0.552631579

Combine like terms: 1.252421477 + 0.552631579 = 1.805053056
x = 1.805053056

Simplifying
x = 1.805053056

Subproblem 2
x + -0.552631579 = -1.252421477

Simplifying
x + -0.552631579 = -1.252421477

Reorder the terms:
-0.552631579 + x = -1.252421477

Solving
-0.552631579 + x = -1.252421477

Solving for variable 'x'.

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

Add '0.552631579' to each side of the equation.
-0.552631579 + 0.552631579 + x = -1.252421477 + 0.552631579

Combine like terms: -0.552631579 + 0.552631579 = 0.000000000
0.000000000 + x = -1.252421477 + 0.552631579
x = -1.252421477 + 0.552631579

Combine like terms: -1.252421477 + 0.552631579 = -0.699789898
x = -0.699789898

Simplifying
x = -0.699789898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.805053056, -0.699789898}