2x(x-7)=12

Solution for 2x(x-7)=12 equation:

Simplifying
2x(x + -7) = 12

Reorder the terms:
2x(-7 + x) = 12
(-7 * 2x + x * 2x) = 12
(-14x + 2x2) = 12

Solving
-14x + 2x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -14x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -7x + x2)' equal to zero and attempt to solve:

Simplifying
-6 + -7x + x2 = 0

Solving
-6 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7x + x2 = 0 + 6
-7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7x + x2 = 6

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7x + x2 = 18.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + -3.5 = 4.272001873

Simplifying
x + -3.5 = 4.272001873

Reorder the terms:
-3.5 + x = 4.272001873

Solving
-3.5 + x = 4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.272001873 + 3.5
x = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
x = 7.772001873

Simplifying
x = 7.772001873

Subproblem 2
x + -3.5 = -4.272001873

Simplifying
x + -3.5 = -4.272001873

Reorder the terms:
-3.5 + x = -4.272001873

Solving
-3.5 + x = -4.272001873

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.272001873 + 3.5
x = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
x = -0.772001873

Simplifying
x = -0.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.772001873, -0.772001873}
Solution
x = {7.772001873, -0.772001873}