3x(6-2x)=27

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Solution for 3x(6-2x)=27 equation: 


Simplifying
3x(6 + -2x) = 27
(6 * 3x + -2x * 3x) = 27
(18x + -6x2) = 27

Solving
18x + -6x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 18x + -6x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 6x + -2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + 6x + -2x2)' equal to zero and attempt to solve:

Simplifying
-9 + 6x + -2x2 = 0

Solving
-9 + 6x + -2x2 = 0

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

Divide each side by '-2'.
4.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -3x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -3x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -3x + x2 = 0 + -4.5
-3x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-3x + x2 = -4.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -4.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -4.5 + 2.25

Combine like terms: -4.5 + 2.25 = -2.25
2.25 + -3x + x2 = -2.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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