18=(3x+2)(2x-6)

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Solution for 18=(3x+2)(2x-6) equation: 


Simplifying
18 = (3x + 2)(2x + -6)

Reorder the terms:
18 = (2 + 3x)(2x + -6)

Reorder the terms:
18 = (2 + 3x)(-6 + 2x)

Multiply (2 + 3x) * (-6 + 2x)
18 = (2(-6 + 2x) + 3x * (-6 + 2x))
18 = ((-6 * 2 + 2x * 2) + 3x * (-6 + 2x))
18 = ((-12 + 4x) + 3x * (-6 + 2x))
18 = (-12 + 4x + (-6 * 3x + 2x * 3x))
18 = (-12 + 4x + (-18x + 6x2))

Combine like terms: 4x + -18x = -14x
18 = (-12 + -14x + 6x2)

Solving
18 = -12 + -14x + 6x2

Solving for variable 'x'.

Combine like terms: 18 + 12 = 30
30 + 14x + -6x2 = -12 + -14x + 6x2 + 12 + 14x + -6x2

Reorder the terms:
30 + 14x + -6x2 = -12 + 12 + -14x + 14x + 6x2 + -6x2

Combine like terms: -12 + 12 = 0
30 + 14x + -6x2 = 0 + -14x + 14x + 6x2 + -6x2
30 + 14x + -6x2 = -14x + 14x + 6x2 + -6x2

Combine like terms: -14x + 14x = 0
30 + 14x + -6x2 = 0 + 6x2 + -6x2
30 + 14x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
30 + 14x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 7x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 7x + -3x2)' equal to zero and attempt to solve:

Simplifying
15 + 7x + -3x2 = 0

Solving
15 + 7x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-5 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -2.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2.333333333x + x2 = 0 + 5
-2.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2.333333333x + x2 = 5

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 5 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 5 + 1.361111112

Combine like terms: 5 + 1.361111112 = 6.361111112
1.361111112 + -2.333333333x + x2 = 6.361111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 6.361111112

Calculate the square root of the right side: 2.522124325

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.522124325 and -2.522124325.


Subproblem 1
x + -1.166666667 = 2.522124325

Simplifying
x + -1.166666667 = 2.522124325

Reorder the terms:
-1.166666667 + x = 2.522124325

Solving
-1.166666667 + x = 2.522124325

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 2.522124325 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 2.522124325 + 1.166666667
x = 2.522124325 + 1.166666667

Combine like terms: 2.522124325 + 1.166666667 = 3.688790992
x = 3.688790992

Simplifying
x = 3.688790992


Subproblem 2
x + -1.166666667 = -2.522124325

Simplifying
x + -1.166666667 = -2.522124325

Reorder the terms:
-1.166666667 + x = -2.522124325

Solving
-1.166666667 + x = -2.522124325

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -2.522124325 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -2.522124325 + 1.166666667
x = -2.522124325 + 1.166666667

Combine like terms: -2.522124325 + 1.166666667 = -1.355457658
x = -1.355457658

Simplifying
x = -1.355457658


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.688790992, -1.355457658}
Solution
x = {3.688790992, -1.355457658}

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