-3x(x-6)=6

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


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

Reorder the terms:
-3x(-6 + x) = 6
(-6 * -3x + x * -3x) = 6
(18x + -3x2) = 6

Solving
18x + -3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 18x + -3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 6x + -1x2) = 0

Ignore the factor 3.

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

Simplifying
-2 + 6x + -1x2 = 0

Solving
-2 + 6x + -1x2 = 0

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

Divide each side by '-1'.
2 + -6x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -6x + x2 = 0 + -2
-6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-6x + x2 = -2

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + -6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + -6x + x2 = 7

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -3) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -3 = 2.645751311

Simplifying
x + -3 = 2.645751311

Reorder the terms:
-3 + x = 2.645751311

Solving
-3 + x = 2.645751311

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.645751311 + 3
x = 2.645751311 + 3

Combine like terms: 2.645751311 + 3 = 5.645751311
x = 5.645751311

Simplifying
x = 5.645751311


Subproblem 2
x + -3 = -2.645751311

Simplifying
x + -3 = -2.645751311

Reorder the terms:
-3 + x = -2.645751311

Solving
-3 + x = -2.645751311

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.645751311 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.645751311 + 3
x = -2.645751311 + 3

Combine like terms: -2.645751311 + 3 = 0.354248689
x = 0.354248689

Simplifying
x = 0.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.645751311, 0.354248689}
Solution
x = {5.645751311, 0.354248689}

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