3x(x-4)=20

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Solution for 3x(x-4)=20 equation: 


Simplifying
3x(x + -4) = 20

Reorder the terms:
3x(-4 + x) = 20
(-4 * 3x + x * 3x) = 20
(-12x + 3x2) = 20

Solving
-12x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -12x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -12x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -4x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -4x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + 6.666666667
-4x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-4x + x2 = 6.666666667

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 = 6.666666667 + 4

Reorder the terms:
4 + -4x + x2 = 6.666666667 + 4

Combine like terms: 6.666666667 + 4 = 10.666666667
4 + -4x + x2 = 10.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(x + -2) equal to 3.265986324 and -3.265986324.


Subproblem 1
x + -2 = 3.265986324

Simplifying
x + -2 = 3.265986324

Reorder the terms:
-2 + x = 3.265986324

Solving
-2 + x = 3.265986324

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 = 3.265986324 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.265986324 + 2
x = 3.265986324 + 2

Combine like terms: 3.265986324 + 2 = 5.265986324
x = 5.265986324

Simplifying
x = 5.265986324


Subproblem 2
x + -2 = -3.265986324

Simplifying
x + -2 = -3.265986324

Reorder the terms:
-2 + x = -3.265986324

Solving
-2 + x = -3.265986324

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 = -3.265986324 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.265986324 + 2
x = -3.265986324 + 2

Combine like terms: -3.265986324 + 2 = -1.265986324
x = -1.265986324

Simplifying
x = -1.265986324


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.265986324, -1.265986324}

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