8x(7x+4)=2

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

Simplifying
8x(7x + 4) = 2

Reorder the terms:
8x(4 + 7x) = 2
(4 * 8x + 7x * 8x) = 2
(32x + 56x2) = 2

Solving
32x + 56x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + 32x + 56x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 32x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 16x + 28x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 16x + 28x2)' equal to zero and attempt to solve:

Simplifying
-1 + 16x + 28x2 = 0

Solving
-1 + 16x + 28x2 = 0

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

Divide each side by '28'.
-0.03571428571 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '0.03571428571' to each side of the equation.
-0.03571428571 + 0.5714285714x + 0.03571428571 + x2 = 0 + 0.03571428571

Reorder the terms:
-0.03571428571 + 0.03571428571 + 0.5714285714x + x2 = 0 + 0.03571428571

Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000
0.00000000000 + 0.5714285714x + x2 = 0 + 0.03571428571
0.5714285714x + x2 = 0 + 0.03571428571

Combine like terms: 0 + 0.03571428571 = 0.03571428571
0.5714285714x + x2 = 0.03571428571

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 0.03571428571 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 0.03571428571 + 0.08163265305

Combine like terms: 0.03571428571 + 0.08163265305 = 0.11734693876
0.08163265305 + 0.5714285714x + x2 = 0.11734693876

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 0.11734693876

Calculate the square root of the right side: 0.342559395

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 0.342559395 and -0.342559395.

Subproblem 1
x + 0.2857142857 = 0.342559395

Simplifying
x + 0.2857142857 = 0.342559395

Reorder the terms:
0.2857142857 + x = 0.342559395

Solving
0.2857142857 + x = 0.342559395

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 0.342559395 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 0.342559395 + -0.2857142857
x = 0.342559395 + -0.2857142857

Combine like terms: 0.342559395 + -0.2857142857 = 0.0568451093
x = 0.0568451093

Simplifying
x = 0.0568451093

Subproblem 2
x + 0.2857142857 = -0.342559395

Simplifying
x + 0.2857142857 = -0.342559395

Reorder the terms:
0.2857142857 + x = -0.342559395

Solving
0.2857142857 + x = -0.342559395

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -0.342559395 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -0.342559395 + -0.2857142857
x = -0.342559395 + -0.2857142857

Combine like terms: -0.342559395 + -0.2857142857 = -0.6282736807
x = -0.6282736807

Simplifying
x = -0.6282736807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0568451093, -0.6282736807}
Solution
x = {0.0568451093, -0.6282736807}