2x(x-12)=40

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Solution for 2x(x-12)=40 equation: 


Simplifying
2x(x + -12) = 40

Reorder the terms:
2x(-12 + x) = 40
(-12 * 2x + x * 2x) = 40
(-24x + 2x2) = 40

Solving
-24x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + -24x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -12x + x2 = 0

Solving
-20 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -12x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -12x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -12x + x2 = 0 + 20
-12x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-12x + x2 = 20

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 20 + 36

Reorder the terms:
36 + -12x + x2 = 20 + 36

Combine like terms: 20 + 36 = 56
36 + -12x + x2 = 56

Factor a perfect square on the left side:
(x + -6)(x + -6) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + -6) equal to 7.483314774 and -7.483314774.


Subproblem 1
x + -6 = 7.483314774

Simplifying
x + -6 = 7.483314774

Reorder the terms:
-6 + x = 7.483314774

Solving
-6 + x = 7.483314774

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 7.483314774 + 6

Combine like terms: -6 + 6 = 0
0 + x = 7.483314774 + 6
x = 7.483314774 + 6

Combine like terms: 7.483314774 + 6 = 13.483314774
x = 13.483314774

Simplifying
x = 13.483314774


Subproblem 2
x + -6 = -7.483314774

Simplifying
x + -6 = -7.483314774

Reorder the terms:
-6 + x = -7.483314774

Solving
-6 + x = -7.483314774

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -7.483314774 + 6

Combine like terms: -6 + 6 = 0
0 + x = -7.483314774 + 6
x = -7.483314774 + 6

Combine like terms: -7.483314774 + 6 = -1.483314774
x = -1.483314774

Simplifying
x = -1.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.483314774, -1.483314774}
Solution
x = {13.483314774, -1.483314774}

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