2(4x-3)4x=78

Solution for 2(4x-3)4x=78 equation:

Simplifying
2(4x + -3) * 4x = 78

Reorder the terms:
2(-3 + 4x) * 4x = 78

Reorder the terms for easier multiplication:
2 * 4x(-3 + 4x) = 78

Multiply 2 * 4
8x(-3 + 4x) = 78
(-3 * 8x + 4x * 8x) = 78
(-24x + 32x2) = 78

Solving
-24x + 32x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + -24x + 32x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + -24x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + -12x + 16x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-39 + -12x + 16x2)' equal to zero and attempt to solve:

Simplifying
-39 + -12x + 16x2 = 0

Solving
-39 + -12x + 16x2 = 0

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

Divide each side by '16'.
-2.4375 + -0.75x + x2 = 0

Move the constant term to the right:

Add '2.4375' to each side of the equation.
-2.4375 + -0.75x + 2.4375 + x2 = 0 + 2.4375

Reorder the terms:
-2.4375 + 2.4375 + -0.75x + x2 = 0 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + -0.75x + x2 = 0 + 2.4375
-0.75x + x2 = 0 + 2.4375

Combine like terms: 0 + 2.4375 = 2.4375
-0.75x + x2 = 2.4375

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 = 2.4375 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 2.4375 + 0.140625

Combine like terms: 2.4375 + 0.140625 = 2.578125
0.140625 + -0.75x + x2 = 2.578125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 2.578125

Calculate the square root of the right side: 1.605654072

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.605654072 and -1.605654072.

Subproblem 1
x + -0.375 = 1.605654072

Simplifying
x + -0.375 = 1.605654072

Reorder the terms:
-0.375 + x = 1.605654072

Solving
-0.375 + x = 1.605654072

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 = 1.605654072 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.605654072 + 0.375
x = 1.605654072 + 0.375

Combine like terms: 1.605654072 + 0.375 = 1.980654072
x = 1.980654072

Simplifying
x = 1.980654072

Subproblem 2
x + -0.375 = -1.605654072

Simplifying
x + -0.375 = -1.605654072

Reorder the terms:
-0.375 + x = -1.605654072

Solving
-0.375 + x = -1.605654072

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 = -1.605654072 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.605654072 + 0.375
x = -1.605654072 + 0.375

Combine like terms: -1.605654072 + 0.375 = -1.230654072
x = -1.230654072

Simplifying
x = -1.230654072

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.980654072, -1.230654072}
Solution
x = {1.980654072, -1.230654072}