18+6x-12=-4(2-x)9x

Solution for 18+6x-12=-4(2-x)9x equation:

Simplifying
18 + 6x + -12 = -4(2 + -1x) * 9x

Reorder the terms:
18 + -12 + 6x = -4(2 + -1x) * 9x

Combine like terms: 18 + -12 = 6
6 + 6x = -4(2 + -1x) * 9x

Reorder the terms for easier multiplication:
6 + 6x = -4 * 9x(2 + -1x)

Multiply -4 * 9
6 + 6x = -36x(2 + -1x)
6 + 6x = (2 * -36x + -1x * -36x)
6 + 6x = (-72x + 36x2)

Solving
6 + 6x = -72x + 36x2

Solving for variable 'x'.

Combine like terms: 6x + 72x = 78x
6 + 78x + -36x2 = -72x + 36x2 + 72x + -36x2

Reorder the terms:
6 + 78x + -36x2 = -72x + 72x + 36x2 + -36x2

Combine like terms: -72x + 72x = 0
6 + 78x + -36x2 = 0 + 36x2 + -36x2
6 + 78x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
6 + 78x + -36x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 13x + -6x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + 13x + -6x2)' equal to zero and attempt to solve:

Simplifying
1 + 13x + -6x2 = 0

Solving
1 + 13x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.1666666667 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -2.166666667x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -2.166666667x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -2.166666667x + x2 = 0 + 0.1666666667
-2.166666667x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-2.166666667x + x2 = 0.1666666667

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = 0.1666666667 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = 0.1666666667 + 1.173611113

Combine like terms: 0.1666666667 + 1.173611113 = 1.3402777797
1.173611113 + -2.166666667x + x2 = 1.3402777797

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 1.3402777797

Calculate the square root of the right side: 1.157703667

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 1.157703667 and -1.157703667.

Subproblem 1
x + -1.083333334 = 1.157703667

Simplifying
x + -1.083333334 = 1.157703667

Reorder the terms:
-1.083333334 + x = 1.157703667

Solving
-1.083333334 + x = 1.157703667

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = 1.157703667 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = 1.157703667 + 1.083333334
x = 1.157703667 + 1.083333334

Combine like terms: 1.157703667 + 1.083333334 = 2.241037001
x = 2.241037001

Simplifying
x = 2.241037001

Subproblem 2
x + -1.083333334 = -1.157703667

Simplifying
x + -1.083333334 = -1.157703667

Reorder the terms:
-1.083333334 + x = -1.157703667

Solving
-1.083333334 + x = -1.157703667

Solving for variable 'x'.

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

Add '1.083333334' to each side of the equation.
-1.083333334 + 1.083333334 + x = -1.157703667 + 1.083333334

Combine like terms: -1.083333334 + 1.083333334 = 0.000000000
0.000000000 + x = -1.157703667 + 1.083333334
x = -1.157703667 + 1.083333334

Combine like terms: -1.157703667 + 1.083333334 = -0.074370333
x = -0.074370333

Simplifying
x = -0.074370333

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.241037001, -0.074370333}
Solution
x = {2.241037001, -0.074370333}