69=(2)(x+2)(x)

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

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

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

Reorder the terms for easier multiplication:
69 = 2x(2 + x)
69 = (2 * 2x + x * 2x)
69 = (4x + 2x2)

Solving
69 = 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
69 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
69 + -4x + -2x2 = 0 + 2x2 + -2x2
69 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
69 + -4x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-34.5 + 2x + x2 = 0

Move the constant term to the right:

Add '34.5' to each side of the equation.
-34.5 + 2x + 34.5 + x2 = 0 + 34.5

Reorder the terms:
-34.5 + 34.5 + 2x + x2 = 0 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + 2x + x2 = 0 + 34.5
2x + x2 = 0 + 34.5

Combine like terms: 0 + 34.5 = 34.5
2x + x2 = 34.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 34.5 + 1

Reorder the terms:
1 + 2x + x2 = 34.5 + 1

Combine like terms: 34.5 + 1 = 35.5
1 + 2x + x2 = 35.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 35.5

Calculate the square root of the right side: 5.958187644

Break this problem into two subproblems by setting 
(x + 1) equal to 5.958187644 and -5.958187644.

Subproblem 1
x + 1 = 5.958187644

Simplifying
x + 1 = 5.958187644

Reorder the terms:
1 + x = 5.958187644

Solving
1 + x = 5.958187644

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 5.958187644 + -1

Combine like terms: 1 + -1 = 0
0 + x = 5.958187644 + -1
x = 5.958187644 + -1

Combine like terms: 5.958187644 + -1 = 4.958187644
x = 4.958187644

Simplifying
x = 4.958187644

Subproblem 2
x + 1 = -5.958187644

Simplifying
x + 1 = -5.958187644

Reorder the terms:
1 + x = -5.958187644

Solving
1 + x = -5.958187644

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -5.958187644 + -1

Combine like terms: 1 + -1 = 0
0 + x = -5.958187644 + -1
x = -5.958187644 + -1

Combine like terms: -5.958187644 + -1 = -6.958187644
x = -6.958187644

Simplifying
x = -6.958187644

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.958187644, -6.958187644}