6(4x-3)2x=70

Solution for 6(4x-3)2x=70 equation:

Simplifying
6(4x + -3) * 2x = 70

Reorder the terms:
6(-3 + 4x) * 2x = 70

Reorder the terms for easier multiplication:
6 * 2x(-3 + 4x) = 70

Multiply 6 * 2
12x(-3 + 4x) = 70
(-3 * 12x + 4x * 12x) = 70
(-36x + 48x2) = 70

Solving
-36x + 48x2 = 70

Solving for variable 'x'.

Reorder the terms:
-70 + -36x + 48x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-70 + -36x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -18x + 24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + -18x + 24x2)' equal to zero and attempt to solve:

Simplifying
-35 + -18x + 24x2 = 0

Solving
-35 + -18x + 24x2 = 0

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

Divide each side by '24'.
-1.458333333 + -0.75x + x2 = 0

Move the constant term to the right:

Add '1.458333333' to each side of the equation.
-1.458333333 + -0.75x + 1.458333333 + x2 = 0 + 1.458333333

Reorder the terms:
-1.458333333 + 1.458333333 + -0.75x + x2 = 0 + 1.458333333

Combine like terms: -1.458333333 + 1.458333333 = 0.000000000
0.000000000 + -0.75x + x2 = 0 + 1.458333333
-0.75x + x2 = 0 + 1.458333333

Combine like terms: 0 + 1.458333333 = 1.458333333
-0.75x + x2 = 1.458333333

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.458333333 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.458333333 + 0.140625

Combine like terms: 1.458333333 + 0.140625 = 1.598958333
0.140625 + -0.75x + x2 = 1.598958333

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.598958333

Calculate the square root of the right side: 1.264499242

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.264499242 and -1.264499242.

Subproblem 1
x + -0.375 = 1.264499242

Simplifying
x + -0.375 = 1.264499242

Reorder the terms:
-0.375 + x = 1.264499242

Solving
-0.375 + x = 1.264499242

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.264499242 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.264499242 + 0.375
x = 1.264499242 + 0.375

Combine like terms: 1.264499242 + 0.375 = 1.639499242
x = 1.639499242

Simplifying
x = 1.639499242

Subproblem 2
x + -0.375 = -1.264499242

Simplifying
x + -0.375 = -1.264499242

Reorder the terms:
-0.375 + x = -1.264499242

Solving
-0.375 + x = -1.264499242

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.264499242 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.264499242 + 0.375
x = -1.264499242 + 0.375

Combine like terms: -1.264499242 + 0.375 = -0.889499242
x = -0.889499242

Simplifying
x = -0.889499242

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.639499242, -0.889499242}
Solution
x = {1.639499242, -0.889499242}