(7x+2)(7x+2)2+6(7x+2)=27

Solution for (7x+2)(7x+2)2+6(7x+2)=27 equation:

Simplifying
(7x + 2)(7x + 2) * 2 + 6(7x + 2) = 27

Reorder the terms:
(2 + 7x)(7x + 2) * 2 + 6(7x + 2) = 27

Reorder the terms:
(2 + 7x)(2 + 7x) * 2 + 6(7x + 2) = 27

Reorder the terms for easier multiplication:
2(2 + 7x)(2 + 7x) + 6(7x + 2) = 27

Multiply (2 + 7x) * (2 + 7x)
2(2(2 + 7x) + 7x * (2 + 7x)) + 6(7x + 2) = 27
2((2 * 2 + 7x * 2) + 7x * (2 + 7x)) + 6(7x + 2) = 27
2((4 + 14x) + 7x * (2 + 7x)) + 6(7x + 2) = 27
2(4 + 14x + (2 * 7x + 7x * 7x)) + 6(7x + 2) = 27
2(4 + 14x + (14x + 49x2)) + 6(7x + 2) = 27

Combine like terms: 14x + 14x = 28x
2(4 + 28x + 49x2) + 6(7x + 2) = 27
(4 * 2 + 28x * 2 + 49x2 * 2) + 6(7x + 2) = 27
(8 + 56x + 98x2) + 6(7x + 2) = 27

Reorder the terms:
8 + 56x + 98x2 + 6(2 + 7x) = 27
8 + 56x + 98x2 + (2 * 6 + 7x * 6) = 27
8 + 56x + 98x2 + (12 + 42x) = 27

Reorder the terms:
8 + 12 + 56x + 42x + 98x2 = 27

Combine like terms: 8 + 12 = 20
20 + 56x + 42x + 98x2 = 27

Combine like terms: 56x + 42x = 98x
20 + 98x + 98x2 = 27

Solving
20 + 98x + 98x2 = 27

Solving for variable 'x'.

Reorder the terms:
20 + -27 + 98x + 98x2 = 27 + -27

Combine like terms: 20 + -27 = -7
-7 + 98x + 98x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-7 + 98x + 98x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + 14x + 14x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-1 + 14x + 14x2)' equal to zero and attempt to solve:

Simplifying
-1 + 14x + 14x2 = 0

Solving
-1 + 14x + 14x2 = 0

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

Divide each side by '14'.
-0.07142857143 + x + x2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + x + 0.07142857143 + x2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + x + x2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + x + x2 = 0 + 0.07142857143
x + x2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
x + x2 = 0.07142857143

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.07142857143 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.07142857143 + 0.25

Combine like terms: 0.07142857143 + 0.25 = 0.32142857143
1.25 + x2 = 0.32142857143

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.32142857143

Calculate the square root of the right side: 0.56694671

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.56694671 and -0.56694671.

Subproblem 1
x + 0.5 = 0.56694671

Simplifying
x + 0.5 = 0.56694671

Reorder the terms:
0.5 + x = 0.56694671

Solving
0.5 + x = 0.56694671

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.56694671 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.56694671 + -0.5
x = 0.56694671 + -0.5

Combine like terms: 0.56694671 + -0.5 = 0.06694671
x = 0.06694671

Simplifying
x = 0.06694671

Subproblem 2
x + 0.5 = -0.56694671

Simplifying
x + 0.5 = -0.56694671

Reorder the terms:
0.5 + x = -0.56694671

Solving
0.5 + x = -0.56694671

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.56694671 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.56694671 + -0.5
x = -0.56694671 + -0.5

Combine like terms: -0.56694671 + -0.5 = -1.06694671
x = -1.06694671

Simplifying
x = -1.06694671

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.06694671, -1.06694671}
Solution
x = {0.06694671, -1.06694671}