7(3x+6)(x+2)=11

Solution for 7(3x+6)(x+2)=11 equation:

Simplifying
7(3x + 6)(x + 2) = 11

Reorder the terms:
7(6 + 3x)(x + 2) = 11

Reorder the terms:
7(6 + 3x)(2 + x) = 11

Multiply (6 + 3x) * (2 + x)
7(6(2 + x) + 3x * (2 + x)) = 11
7((2 * 6 + x * 6) + 3x * (2 + x)) = 11
7((12 + 6x) + 3x * (2 + x)) = 11
7(12 + 6x + (2 * 3x + x * 3x)) = 11
7(12 + 6x + (6x + 3x2)) = 11

Combine like terms: 6x + 6x = 12x
7(12 + 12x + 3x2) = 11
(12 * 7 + 12x * 7 + 3x2 * 7) = 11
(84 + 84x + 21x2) = 11

Solving
84 + 84x + 21x2 = 11

Solving for variable 'x'.

Reorder the terms:
84 + -11 + 84x + 21x2 = 11 + -11

Combine like terms: 84 + -11 = 73
73 + 84x + 21x2 = 11 + -11

Combine like terms: 11 + -11 = 0
73 + 84x + 21x2 = 0

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

Divide each side by '21'.
3.476190476 + 4x + x2 = 0

Move the constant term to the right:

Add '-3.476190476' to each side of the equation.
3.476190476 + 4x + -3.476190476 + x2 = 0 + -3.476190476

Reorder the terms:
3.476190476 + -3.476190476 + 4x + x2 = 0 + -3.476190476

Combine like terms: 3.476190476 + -3.476190476 = 0.000000000
0.000000000 + 4x + x2 = 0 + -3.476190476
4x + x2 = 0 + -3.476190476

Combine like terms: 0 + -3.476190476 = -3.476190476
4x + x2 = -3.476190476

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -3.476190476 + 4

Reorder the terms:
4 + 4x + x2 = -3.476190476 + 4

Combine like terms: -3.476190476 + 4 = 0.523809524
4 + 4x + x2 = 0.523809524

Factor a perfect square on the left side:
(x + 2)(x + 2) = 0.523809524

Calculate the square root of the right side: 0.723746865

Break this problem into two subproblems by setting 
(x + 2) equal to 0.723746865 and -0.723746865.

Subproblem 1
x + 2 = 0.723746865

Simplifying
x + 2 = 0.723746865

Reorder the terms:
2 + x = 0.723746865

Solving
2 + x = 0.723746865

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 0.723746865 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0.723746865 + -2
x = 0.723746865 + -2

Combine like terms: 0.723746865 + -2 = -1.276253135
x = -1.276253135

Simplifying
x = -1.276253135

Subproblem 2
x + 2 = -0.723746865

Simplifying
x + 2 = -0.723746865

Reorder the terms:
2 + x = -0.723746865

Solving
2 + x = -0.723746865

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -0.723746865 + -2

Combine like terms: 2 + -2 = 0
0 + x = -0.723746865 + -2
x = -0.723746865 + -2

Combine like terms: -0.723746865 + -2 = -2.723746865
x = -2.723746865

Simplifying
x = -2.723746865

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.276253135, -2.723746865}