(x+5)(3x-6)=9

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Solution for (x+5)(3x-6)=9 equation: 


Simplifying
(x + 5)(3x + -6) = 9

Reorder the terms:
(5 + x)(3x + -6) = 9

Reorder the terms:
(5 + x)(-6 + 3x) = 9

Multiply (5 + x) * (-6 + 3x)
(5(-6 + 3x) + x(-6 + 3x)) = 9
((-6 * 5 + 3x * 5) + x(-6 + 3x)) = 9
((-30 + 15x) + x(-6 + 3x)) = 9
(-30 + 15x + (-6 * x + 3x * x)) = 9
(-30 + 15x + (-6x + 3x2)) = 9

Combine like terms: 15x + -6x = 9x
(-30 + 9x + 3x2) = 9

Solving
-30 + 9x + 3x2 = 9

Solving for variable 'x'.

Reorder the terms:
-30 + -9 + 9x + 3x2 = 9 + -9

Combine like terms: -30 + -9 = -39
-39 + 9x + 3x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-39 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-13 + 3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-13 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + 3x + x2 = 0

Solving
-13 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 3x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 3x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3x + x2 = 0 + 13
3x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
3x + x2 = 13

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 13 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 13 + 2.25

Combine like terms: 13 + 2.25 = 15.25
2.25 + 3x + x2 = 15.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 1.5 = 3.905124838

Simplifying
x + 1.5 = 3.905124838

Reorder the terms:
1.5 + x = 3.905124838

Solving
1.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.905124838 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.905124838 + -1.5
x = 3.905124838 + -1.5

Combine like terms: 3.905124838 + -1.5 = 2.405124838
x = 2.405124838

Simplifying
x = 2.405124838


Subproblem 2
x + 1.5 = -3.905124838

Simplifying
x + 1.5 = -3.905124838

Reorder the terms:
1.5 + x = -3.905124838

Solving
1.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.905124838 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.905124838 + -1.5
x = -3.905124838 + -1.5

Combine like terms: -3.905124838 + -1.5 = -5.405124838
x = -5.405124838

Simplifying
x = -5.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.405124838, -5.405124838}
Solution
x = {2.405124838, -5.405124838}

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