(2x-4)(3x+8)=18

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Solution for (2x-4)(3x+8)=18 equation: 


Simplifying
(2x + -4)(3x + 8) = 18

Reorder the terms:
(-4 + 2x)(3x + 8) = 18

Reorder the terms:
(-4 + 2x)(8 + 3x) = 18

Multiply (-4 + 2x) * (8 + 3x)
(-4(8 + 3x) + 2x * (8 + 3x)) = 18
((8 * -4 + 3x * -4) + 2x * (8 + 3x)) = 18
((-32 + -12x) + 2x * (8 + 3x)) = 18
(-32 + -12x + (8 * 2x + 3x * 2x)) = 18
(-32 + -12x + (16x + 6x2)) = 18

Combine like terms: -12x + 16x = 4x
(-32 + 4x + 6x2) = 18

Solving
-32 + 4x + 6x2 = 18

Solving for variable 'x'.

Reorder the terms:
-32 + -18 + 4x + 6x2 = 18 + -18

Combine like terms: -32 + -18 = -50
-50 + 4x + 6x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-50 + 4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 2x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + 2x + 3x2)' equal to zero and attempt to solve:

Simplifying
-25 + 2x + 3x2 = 0

Solving
-25 + 2x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 0.6666666667x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 0.6666666667x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 8.333333333
0.6666666667x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
0.6666666667x + x2 = 8.333333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 8.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 8.333333333 + 0.1111111112

Combine like terms: 8.333333333 + 0.1111111112 = 8.4444444442
0.1111111112 + 0.6666666667x + x2 = 8.4444444442

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 8.4444444442

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 2.905932629 and -2.905932629.


Subproblem 1
x + 0.3333333334 = 2.905932629

Simplifying
x + 0.3333333334 = 2.905932629

Reorder the terms:
0.3333333334 + x = 2.905932629

Solving
0.3333333334 + x = 2.905932629

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 2.905932629 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 2.905932629 + -0.3333333334
x = 2.905932629 + -0.3333333334

Combine like terms: 2.905932629 + -0.3333333334 = 2.5725992956
x = 2.5725992956

Simplifying
x = 2.5725992956


Subproblem 2
x + 0.3333333334 = -2.905932629

Simplifying
x + 0.3333333334 = -2.905932629

Reorder the terms:
0.3333333334 + x = -2.905932629

Solving
0.3333333334 + x = -2.905932629

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -2.905932629 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -2.905932629 + -0.3333333334
x = -2.905932629 + -0.3333333334

Combine like terms: -2.905932629 + -0.3333333334 = -3.2392659624
x = -3.2392659624

Simplifying
x = -3.2392659624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5725992956, -3.2392659624}
Solution
x = {2.5725992956, -3.2392659624}

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