(2x+1)(3x+1)=69(x+1)

Solution for (2x+1)(3x+1)=69(x+1) equation:

Simplifying
(2x + 1)(3x + 1) = 69(x + 1)

Reorder the terms:
(1 + 2x)(3x + 1) = 69(x + 1)

Reorder the terms:
(1 + 2x)(1 + 3x) = 69(x + 1)

Multiply (1 + 2x) * (1 + 3x)
(1(1 + 3x) + 2x * (1 + 3x)) = 69(x + 1)
((1 * 1 + 3x * 1) + 2x * (1 + 3x)) = 69(x + 1)
((1 + 3x) + 2x * (1 + 3x)) = 69(x + 1)
(1 + 3x + (1 * 2x + 3x * 2x)) = 69(x + 1)
(1 + 3x + (2x + 6x2)) = 69(x + 1)

Combine like terms: 3x + 2x = 5x
(1 + 5x + 6x2) = 69(x + 1)

Reorder the terms:
1 + 5x + 6x2 = 69(1 + x)
1 + 5x + 6x2 = (1 * 69 + x * 69)
1 + 5x + 6x2 = (69 + 69x)

Solving
1 + 5x + 6x2 = 69 + 69x

Solving for variable 'x'.

Reorder the terms:
1 + -69 + 5x + -69x + 6x2 = 69 + 69x + -69 + -69x

Combine like terms: 1 + -69 = -68
-68 + 5x + -69x + 6x2 = 69 + 69x + -69 + -69x

Combine like terms: 5x + -69x = -64x
-68 + -64x + 6x2 = 69 + 69x + -69 + -69x

Reorder the terms:
-68 + -64x + 6x2 = 69 + -69 + 69x + -69x

Combine like terms: 69 + -69 = 0
-68 + -64x + 6x2 = 0 + 69x + -69x
-68 + -64x + 6x2 = 69x + -69x

Combine like terms: 69x + -69x = 0
-68 + -64x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-34 + -32x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-34 + -32x + 3x2)' equal to zero and attempt to solve:

Simplifying
-34 + -32x + 3x2 = 0

Solving
-34 + -32x + 3x2 = 0

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

Divide each side by '3'.
-11.33333333 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '11.33333333' to each side of the equation.
-11.33333333 + -10.66666667x + 11.33333333 + x2 = 0 + 11.33333333

Reorder the terms:
-11.33333333 + 11.33333333 + -10.66666667x + x2 = 0 + 11.33333333

Combine like terms: -11.33333333 + 11.33333333 = 0.00000000
0.00000000 + -10.66666667x + x2 = 0 + 11.33333333
-10.66666667x + x2 = 0 + 11.33333333

Combine like terms: 0 + 11.33333333 = 11.33333333
-10.66666667x + x2 = 11.33333333

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = 11.33333333 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = 11.33333333 + 28.44444446

Combine like terms: 11.33333333 + 28.44444446 = 39.77777779
28.44444446 + -10.66666667x + x2 = 39.77777779

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 39.77777779

Calculate the square root of the right side: 6.306962644

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 6.306962644 and -6.306962644.

Subproblem 1
x + -5.333333335 = 6.306962644

Simplifying
x + -5.333333335 = 6.306962644

Reorder the terms:
-5.333333335 + x = 6.306962644

Solving
-5.333333335 + x = 6.306962644

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 6.306962644 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 6.306962644 + 5.333333335
x = 6.306962644 + 5.333333335

Combine like terms: 6.306962644 + 5.333333335 = 11.640295979
x = 11.640295979

Simplifying
x = 11.640295979

Subproblem 2
x + -5.333333335 = -6.306962644

Simplifying
x + -5.333333335 = -6.306962644

Reorder the terms:
-5.333333335 + x = -6.306962644

Solving
-5.333333335 + x = -6.306962644

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -6.306962644 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -6.306962644 + 5.333333335
x = -6.306962644 + 5.333333335

Combine like terms: -6.306962644 + 5.333333335 = -0.973629309
x = -0.973629309

Simplifying
x = -0.973629309

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.640295979, -0.973629309}
Solution
x = {11.640295979, -0.973629309}