2(x-2)12x-42=

Solution for 2(x-2)12x-42= equation:

Simplifying
2(x + -2) * 12x + -42 = 0

Reorder the terms:
2(-2 + x) * 12x + -42 = 0

Reorder the terms for easier multiplication:
2 * 12x(-2 + x) + -42 = 0

Multiply 2 * 12
24x(-2 + x) + -42 = 0
(-2 * 24x + x * 24x) + -42 = 0
(-48x + 24x2) + -42 = 0

Reorder the terms:
-42 + -48x + 24x2 = 0

Solving
-42 + -48x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -8x + 4x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -8x + 4x2)' equal to zero and attempt to solve:

Simplifying
-7 + -8x + 4x2 = 0

Solving
-7 + -8x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + -2x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -2x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -2x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -2x + x2 = 0 + 1.75
-2x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-2x + x2 = 1.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.75 + 1

Reorder the terms:
1 + -2x + x2 = 1.75 + 1

Combine like terms: 1.75 + 1 = 2.75
1 + -2x + x2 = 2.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -1) equal to 1.658312395 and -1.658312395.

Subproblem 1
x + -1 = 1.658312395

Simplifying
x + -1 = 1.658312395

Reorder the terms:
-1 + x = 1.658312395

Solving
-1 + x = 1.658312395

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.658312395 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.658312395 + 1
x = 1.658312395 + 1

Combine like terms: 1.658312395 + 1 = 2.658312395
x = 2.658312395

Simplifying
x = 2.658312395

Subproblem 2
x + -1 = -1.658312395

Simplifying
x + -1 = -1.658312395

Reorder the terms:
-1 + x = -1.658312395

Solving
-1 + x = -1.658312395

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.658312395 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.658312395 + 1
x = -1.658312395 + 1

Combine like terms: -1.658312395 + 1 = -0.658312395
x = -0.658312395

Simplifying
x = -0.658312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.658312395, -0.658312395}
Solution
x = {2.658312395, -0.658312395}