2x(12-3x)=4

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Solution for 2x(12-3x)=4 equation: 


Simplifying
2x(12 + -3x) = 4
(12 * 2x + -3x * 2x) = 4
(24x + -6x2) = 4

Solving
24x + -6x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 24x + -6x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 12x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 12x + -3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 12x + -3x2 = 0

Solving
-2 + 12x + -3x2 = 0

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

Divide each side by '-3'.
0.6666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -4x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -4x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -4x + x2 = 0 + -0.6666666667
-4x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-4x + x2 = -0.6666666667

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 = -0.6666666667 + 4

Reorder the terms:
4 + -4x + x2 = -0.6666666667 + 4

Combine like terms: -0.6666666667 + 4 = 3.3333333333
4 + -4x + x2 = 3.3333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.3333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(x + -2) equal to 1.825741858 and -1.825741858.


Subproblem 1
x + -2 = 1.825741858

Simplifying
x + -2 = 1.825741858

Reorder the terms:
-2 + x = 1.825741858

Solving
-2 + x = 1.825741858

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 = 1.825741858 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.825741858 + 2
x = 1.825741858 + 2

Combine like terms: 1.825741858 + 2 = 3.825741858
x = 3.825741858

Simplifying
x = 3.825741858


Subproblem 2
x + -2 = -1.825741858

Simplifying
x + -2 = -1.825741858

Reorder the terms:
-2 + x = -1.825741858

Solving
-2 + x = -1.825741858

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 = -1.825741858 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.825741858 + 2
x = -1.825741858 + 2

Combine like terms: -1.825741858 + 2 = 0.174258142
x = 0.174258142

Simplifying
x = 0.174258142


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.825741858, 0.174258142}
Solution
x = {3.825741858, 0.174258142}

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