-3(4x^2-36x)=-6

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Solution for -3(4x^2-36x)=-6 equation: 


Simplifying
-3(4x2 + -36x) = -6

Reorder the terms:
-3(-36x + 4x2) = -6
(-36x * -3 + 4x2 * -3) = -6
(108x + -12x2) = -6

Solving
108x + -12x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 108x + -12x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 108x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 18x + -2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(1 + 18x + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + 18x + -2x2 = 0

Solving
1 + 18x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + -9x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -9x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -9x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -9x + x2 = 0 + 0.5
-9x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-9x + x2 = 0.5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 0.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 0.5 + 20.25

Combine like terms: 0.5 + 20.25 = 20.75
20.25 + -9x + x2 = 20.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 20.75

Calculate the square root of the right side: 4.55521679

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.55521679 and -4.55521679.


Subproblem 1
x + -4.5 = 4.55521679

Simplifying
x + -4.5 = 4.55521679

Reorder the terms:
-4.5 + x = 4.55521679

Solving
-4.5 + x = 4.55521679

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 4.55521679 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.55521679 + 4.5
x = 4.55521679 + 4.5

Combine like terms: 4.55521679 + 4.5 = 9.05521679
x = 9.05521679

Simplifying
x = 9.05521679


Subproblem 2
x + -4.5 = -4.55521679

Simplifying
x + -4.5 = -4.55521679

Reorder the terms:
-4.5 + x = -4.55521679

Solving
-4.5 + x = -4.55521679

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -4.55521679 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.55521679 + 4.5
x = -4.55521679 + 4.5

Combine like terms: -4.55521679 + 4.5 = -0.05521679
x = -0.05521679

Simplifying
x = -0.05521679


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.05521679, -0.05521679}
Solution
x = {9.05521679, -0.05521679}

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