4(x-4)3x=10

Solution for 4(x-4)3x=10 equation:

Simplifying
4(x + -4) * 3x = 10

Reorder the terms:
4(-4 + x) * 3x = 10

Reorder the terms for easier multiplication:
4 * 3x(-4 + x) = 10

Multiply 4 * 3
12x(-4 + x) = 10
(-4 * 12x + x * 12x) = 10
(-48x + 12x2) = 10

Solving
-48x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -48x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -48x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -24x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -24x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + -24x + 6x2 = 0

Solving
-5 + -24x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -4x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -4x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -4x + x2 = 0 + 0.8333333333
-4x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-4x + x2 = 0.8333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 0.8333333333 + 4

Reorder the terms:
4 + -4x + x2 = 0.8333333333 + 4

Combine like terms: 0.8333333333 + 4 = 4.8333333333
4 + -4x + x2 = 4.8333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.8333333333

Calculate the square root of the right side: 2.198484326

Break this problem into two subproblems by setting 
(x + -2) equal to 2.198484326 and -2.198484326.

Subproblem 1
x + -2 = 2.198484326

Simplifying
x + -2 = 2.198484326

Reorder the terms:
-2 + x = 2.198484326

Solving
-2 + x = 2.198484326

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.198484326 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.198484326 + 2
x = 2.198484326 + 2

Combine like terms: 2.198484326 + 2 = 4.198484326
x = 4.198484326

Simplifying
x = 4.198484326

Subproblem 2
x + -2 = -2.198484326

Simplifying
x + -2 = -2.198484326

Reorder the terms:
-2 + x = -2.198484326

Solving
-2 + x = -2.198484326

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.198484326 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.198484326 + 2
x = -2.198484326 + 2

Combine like terms: -2.198484326 + 2 = -0.198484326
x = -0.198484326

Simplifying
x = -0.198484326

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.198484326, -0.198484326}
Solution
x = {4.198484326, -0.198484326}