X(12-3X)=-27

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Solution for X(12-3X)=-27 equation: 


Simplifying
X(12 + -3X) = -27
(12 * X + -3X * X) = -27
(12X + -3X2) = -27

Solving
12X + -3X2 = -27

Solving for variable 'X'.

Reorder the terms:
27 + 12X + -3X2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 12X + -3X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 4X + -1X2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 4X + -1X2)' equal to zero and attempt to solve:

Simplifying
9 + 4X + -1X2 = 0

Solving
9 + 4X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + -4X + X2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -4X + 9 + X2 = 0 + 9

Reorder the terms:
-9 + 9 + -4X + X2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4X + X2 = 0 + 9
-4X + X2 = 0 + 9

Combine like terms: 0 + 9 = 9
-4X + X2 = 9

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 = 9 + 4

Reorder the terms:
4 + -4X + X2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + -4X + X2 = 13

Factor a perfect square on the left side:
(X + -2)(X + -2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(X + -2) equal to 3.605551275 and -3.605551275.


Subproblem 1
X + -2 = 3.605551275

Simplifying
X + -2 = 3.605551275

Reorder the terms:
-2 + X = 3.605551275

Solving
-2 + X = 3.605551275

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 = 3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + X = 3.605551275 + 2
X = 3.605551275 + 2

Combine like terms: 3.605551275 + 2 = 5.605551275
X = 5.605551275

Simplifying
X = 5.605551275


Subproblem 2
X + -2 = -3.605551275

Simplifying
X + -2 = -3.605551275

Reorder the terms:
-2 + X = -3.605551275

Solving
-2 + X = -3.605551275

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 = -3.605551275 + 2

Combine like terms: -2 + 2 = 0
0 + X = -3.605551275 + 2
X = -3.605551275 + 2

Combine like terms: -3.605551275 + 2 = -1.605551275
X = -1.605551275

Simplifying
X = -1.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.605551275, -1.605551275}
Solution
X = {5.605551275, -1.605551275}

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