-3x(x-3)=-6

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


Simplifying
-3x(x + -3) = -6

Reorder the terms:
-3x(-3 + x) = -6
(-3 * -3x + x * -3x) = -6
(9x + -3x2) = -6

Solving
9x + -3x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 9x + -3x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 3x + -1x2) = 0

Ignore the factor 3.

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

Simplifying
2 + 3x + -1x2 = 0

Solving
2 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-2 + -3x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x + x2 = 0 + 2
-3x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3x + x2 = 2

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 = 2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3x + x2 = 4.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
x + -1.5 = 2.061552813

Simplifying
x + -1.5 = 2.061552813

Reorder the terms:
-1.5 + x = 2.061552813

Solving
-1.5 + x = 2.061552813

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 2.061552813 + 1.5
x = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
x = 3.561552813

Simplifying
x = 3.561552813


Subproblem 2
x + -1.5 = -2.061552813

Simplifying
x + -1.5 = -2.061552813

Reorder the terms:
-1.5 + x = -2.061552813

Solving
-1.5 + x = -2.061552813

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -2.061552813 + 1.5
x = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
x = -0.561552813

Simplifying
x = -0.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.561552813, -0.561552813}
Solution
x = {3.561552813, -0.561552813}

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