4x(7x+1)=34x+2(2+8)

Solution for 4x(7x+1)=34x+2(2+8) equation:

Simplifying
4x(7x + 1) = 34x + 2(2 + 8)

Reorder the terms:
4x(1 + 7x) = 34x + 2(2 + 8)
(1 * 4x + 7x * 4x) = 34x + 2(2 + 8)
(4x + 28x2) = 34x + 2(2 + 8)

Combine like terms: 2 + 8 = 10
4x + 28x2 = 34x + 2(10)

Multiply 2 * 10
4x + 28x2 = 34x + 20

Reorder the terms:
4x + 28x2 = 20 + 34x

Solving
4x + 28x2 = 20 + 34x

Solving for variable 'x'.

Reorder the terms:
-20 + 4x + -34x + 28x2 = 20 + 34x + -20 + -34x

Combine like terms: 4x + -34x = -30x
-20 + -30x + 28x2 = 20 + 34x + -20 + -34x

Reorder the terms:
-20 + -30x + 28x2 = 20 + -20 + 34x + -34x

Combine like terms: 20 + -20 = 0
-20 + -30x + 28x2 = 0 + 34x + -34x
-20 + -30x + 28x2 = 34x + -34x

Combine like terms: 34x + -34x = 0
-20 + -30x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -15x + 14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -15x + 14x2)' equal to zero and attempt to solve:

Simplifying
-10 + -15x + 14x2 = 0

Solving
-10 + -15x + 14x2 = 0

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

Divide each side by '14'.
-0.7142857143 + -1.071428571x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -1.071428571x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -1.071428571x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -1.071428571x + x2 = 0 + 0.7142857143
-1.071428571x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-1.071428571x + x2 = 0.7142857143

The x term is -1.071428571x.  Take half its coefficient (-0.5357142855).
Square it (0.2869897957) and add it to both sides.

Add '0.2869897957' to each side of the equation.
-1.071428571x + 0.2869897957 + x2 = 0.7142857143 + 0.2869897957

Reorder the terms:
0.2869897957 + -1.071428571x + x2 = 0.7142857143 + 0.2869897957

Combine like terms: 0.7142857143 + 0.2869897957 = 1.00127551
0.2869897957 + -1.071428571x + x2 = 1.00127551

Factor a perfect square on the left side:
(x + -0.5357142855)(x + -0.5357142855) = 1.00127551

Calculate the square root of the right side: 1.000637552

Break this problem into two subproblems by setting 
(x + -0.5357142855) equal to 1.000637552 and -1.000637552.

Subproblem 1
x + -0.5357142855 = 1.000637552

Simplifying
x + -0.5357142855 = 1.000637552

Reorder the terms:
-0.5357142855 + x = 1.000637552

Solving
-0.5357142855 + x = 1.000637552

Solving for variable 'x'.

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

Add '0.5357142855' to each side of the equation.
-0.5357142855 + 0.5357142855 + x = 1.000637552 + 0.5357142855

Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000
0.0000000000 + x = 1.000637552 + 0.5357142855
x = 1.000637552 + 0.5357142855

Combine like terms: 1.000637552 + 0.5357142855 = 1.5363518375
x = 1.5363518375

Simplifying
x = 1.5363518375

Subproblem 2
x + -0.5357142855 = -1.000637552

Simplifying
x + -0.5357142855 = -1.000637552

Reorder the terms:
-0.5357142855 + x = -1.000637552

Solving
-0.5357142855 + x = -1.000637552

Solving for variable 'x'.

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

Add '0.5357142855' to each side of the equation.
-0.5357142855 + 0.5357142855 + x = -1.000637552 + 0.5357142855

Combine like terms: -0.5357142855 + 0.5357142855 = 0.0000000000
0.0000000000 + x = -1.000637552 + 0.5357142855
x = -1.000637552 + 0.5357142855

Combine like terms: -1.000637552 + 0.5357142855 = -0.4649232665
x = -0.4649232665

Simplifying
x = -0.4649232665

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5363518375, -0.4649232665}
Solution
x = {1.5363518375, -0.4649232665}