2(14x^2-35x+6)=0

Solution for 2(14x^2-35x+6)=0 equation:

Simplifying
2(14x2 + -35x + 6) = 0

Reorder the terms:
2(6 + -35x + 14x2) = 0
(6 * 2 + -35x * 2 + 14x2 * 2) = 0
(12 + -70x + 28x2) = 0

Solving
12 + -70x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -35x + 14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -35x + 14x2)' equal to zero and attempt to solve:

Simplifying
6 + -35x + 14x2 = 0

Solving
6 + -35x + 14x2 = 0

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

Divide each side by '14'.
0.4285714286 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -2.5x + -0.4285714286 + x2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + -2.5x + x2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + -2.5x + x2 = 0 + -0.4285714286
-2.5x + x2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
-2.5x + x2 = -0.4285714286

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -0.4285714286 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -0.4285714286 + 1.5625

Combine like terms: -0.4285714286 + 1.5625 = 1.1339285714
1.5625 + -2.5x + x2 = 1.1339285714

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.1339285714

Calculate the square root of the right side: 1.064860823

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.064860823 and -1.064860823.

Subproblem 1
x + -1.25 = 1.064860823

Simplifying
x + -1.25 = 1.064860823

Reorder the terms:
-1.25 + x = 1.064860823

Solving
-1.25 + x = 1.064860823

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.064860823 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.064860823 + 1.25
x = 1.064860823 + 1.25

Combine like terms: 1.064860823 + 1.25 = 2.314860823
x = 2.314860823

Simplifying
x = 2.314860823

Subproblem 2
x + -1.25 = -1.064860823

Simplifying
x + -1.25 = -1.064860823

Reorder the terms:
-1.25 + x = -1.064860823

Solving
-1.25 + x = -1.064860823

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.064860823 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.064860823 + 1.25
x = -1.064860823 + 1.25

Combine like terms: -1.064860823 + 1.25 = 0.185139177
x = 0.185139177

Simplifying
x = 0.185139177

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.314860823, 0.185139177}
Solution
x = {2.314860823, 0.185139177}