6x(x-12)+18(x-1)=6

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Solution for 6x(x-12)+18(x-1)=6 equation: 


Simplifying
6x(x + -12) + 18(x + -1) = 6

Reorder the terms:
6x(-12 + x) + 18(x + -1) = 6
(-12 * 6x + x * 6x) + 18(x + -1) = 6
(-72x + 6x2) + 18(x + -1) = 6

Reorder the terms:
-72x + 6x2 + 18(-1 + x) = 6
-72x + 6x2 + (-1 * 18 + x * 18) = 6
-72x + 6x2 + (-18 + 18x) = 6

Reorder the terms:
-18 + -72x + 18x + 6x2 = 6

Combine like terms: -72x + 18x = -54x
-18 + -54x + 6x2 = 6

Solving
-18 + -54x + 6x2 = 6

Solving for variable 'x'.

Reorder the terms:
-18 + -6 + -54x + 6x2 = 6 + -6

Combine like terms: -18 + -6 = -24
-24 + -54x + 6x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-24 + -54x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + -9x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + -9x + x2 = 0

Solving
-4 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -9x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -9x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x + x2 = 0 + 4
-9x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-9x + x2 = 4

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 = 4 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 4 + 20.25

Combine like terms: 4 + 20.25 = 24.25
20.25 + -9x + x2 = 24.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + -4.5 = 4.924428901

Simplifying
x + -4.5 = 4.924428901

Reorder the terms:
-4.5 + x = 4.924428901

Solving
-4.5 + x = 4.924428901

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 = 4.924428901 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.924428901 + 4.5
x = 4.924428901 + 4.5

Combine like terms: 4.924428901 + 4.5 = 9.424428901
x = 9.424428901

Simplifying
x = 9.424428901


Subproblem 2
x + -4.5 = -4.924428901

Simplifying
x + -4.5 = -4.924428901

Reorder the terms:
-4.5 + x = -4.924428901

Solving
-4.5 + x = -4.924428901

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 = -4.924428901 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.924428901 + 4.5
x = -4.924428901 + 4.5

Combine like terms: -4.924428901 + 4.5 = -0.424428901
x = -0.424428901

Simplifying
x = -0.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.424428901, -0.424428901}
Solution
x = {9.424428901, -0.424428901}

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