7(x+1)2(6+5x)=7

Solution for 7(x+1)2(6+5x)=7 equation:

Simplifying
7(x + 1) * 2(6 + 5x) = 7

Reorder the terms:
7(1 + x) * 2(6 + 5x) = 7

Reorder the terms for easier multiplication:
7 * 2(1 + x)(6 + 5x) = 7

Multiply 7 * 2
14(1 + x)(6 + 5x) = 7

Multiply (1 + x) * (6 + 5x)
14(1(6 + 5x) + x(6 + 5x)) = 7
14((6 * 1 + 5x * 1) + x(6 + 5x)) = 7
14((6 + 5x) + x(6 + 5x)) = 7
14(6 + 5x + (6 * x + 5x * x)) = 7
14(6 + 5x + (6x + 5x2)) = 7

Combine like terms: 5x + 6x = 11x
14(6 + 11x + 5x2) = 7
(6 * 14 + 11x * 14 + 5x2 * 14) = 7
(84 + 154x + 70x2) = 7

Solving
84 + 154x + 70x2 = 7

Solving for variable 'x'.

Reorder the terms:
84 + -7 + 154x + 70x2 = 7 + -7

Combine like terms: 84 + -7 = 77
77 + 154x + 70x2 = 7 + -7

Combine like terms: 7 + -7 = 0
77 + 154x + 70x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(11 + 22x + 10x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(11 + 22x + 10x2)' equal to zero and attempt to solve:

Simplifying
11 + 22x + 10x2 = 0

Solving
11 + 22x + 10x2 = 0

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

Divide each side by '10'.
1.1 + 2.2x + x2 = 0.0

Move the constant term to the right:

Add '-1.1' to each side of the equation.
1.1 + 2.2x + -1.1 + x2 = 0.0 + -1.1

Reorder the terms:
1.1 + -1.1 + 2.2x + x2 = 0.0 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + 2.2x + x2 = 0.0 + -1.1
2.2x + x2 = 0.0 + -1.1

Combine like terms: 0.0 + -1.1 = -1.1
2.2x + x2 = -1.1

The x term is 2.2x.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2x + 1.21 + x2 = -1.1 + 1.21

Reorder the terms:
1.21 + 2.2x + x2 = -1.1 + 1.21

Combine like terms: -1.1 + 1.21 = 0.11
1.21 + 2.2x + x2 = 0.11

Factor a perfect square on the left side:
(x + 1.1)(x + 1.1) = 0.11

Calculate the square root of the right side: 0.331662479

Break this problem into two subproblems by setting 
(x + 1.1) equal to 0.331662479 and -0.331662479.

Subproblem 1
x + 1.1 = 0.331662479

Simplifying
x + 1.1 = 0.331662479

Reorder the terms:
1.1 + x = 0.331662479

Solving
1.1 + x = 0.331662479

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = 0.331662479 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = 0.331662479 + -1.1
x = 0.331662479 + -1.1

Combine like terms: 0.331662479 + -1.1 = -0.768337521
x = -0.768337521

Simplifying
x = -0.768337521

Subproblem 2
x + 1.1 = -0.331662479

Simplifying
x + 1.1 = -0.331662479

Reorder the terms:
1.1 + x = -0.331662479

Solving
1.1 + x = -0.331662479

Solving for variable 'x'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + x = -0.331662479 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + x = -0.331662479 + -1.1
x = -0.331662479 + -1.1

Combine like terms: -0.331662479 + -1.1 = -1.431662479
x = -1.431662479

Simplifying
x = -1.431662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.768337521, -1.431662479}
Solution
x = {-0.768337521, -1.431662479}