(3x+9)(x+5)=120

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Solution for (3x+9)(x+5)=120 equation: 


Simplifying
(3x + 9)(x + 5) = 120

Reorder the terms:
(9 + 3x)(x + 5) = 120

Reorder the terms:
(9 + 3x)(5 + x) = 120

Multiply (9 + 3x) * (5 + x)
(9(5 + x) + 3x * (5 + x)) = 120
((5 * 9 + x * 9) + 3x * (5 + x)) = 120
((45 + 9x) + 3x * (5 + x)) = 120
(45 + 9x + (5 * 3x + x * 3x)) = 120
(45 + 9x + (15x + 3x2)) = 120

Combine like terms: 9x + 15x = 24x
(45 + 24x + 3x2) = 120

Solving
45 + 24x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
45 + -120 + 24x + 3x2 = 120 + -120

Combine like terms: 45 + -120 = -75
-75 + 24x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-75 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-25 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + 8x + x2 = 0

Solving
-25 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 8x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 8x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 8x + x2 = 0 + 25
8x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
8x + x2 = 25

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 25 + 16

Reorder the terms:
16 + 8x + x2 = 25 + 16

Combine like terms: 25 + 16 = 41
16 + 8x + x2 = 41

Factor a perfect square on the left side:
(x + 4)(x + 4) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 4) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 4 = 6.403124237

Simplifying
x + 4 = 6.403124237

Reorder the terms:
4 + x = 6.403124237

Solving
4 + x = 6.403124237

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.403124237 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.403124237 + -4
x = 6.403124237 + -4

Combine like terms: 6.403124237 + -4 = 2.403124237
x = 2.403124237

Simplifying
x = 2.403124237


Subproblem 2
x + 4 = -6.403124237

Simplifying
x + 4 = -6.403124237

Reorder the terms:
4 + x = -6.403124237

Solving
4 + x = -6.403124237

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.403124237 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.403124237 + -4
x = -6.403124237 + -4

Combine like terms: -6.403124237 + -4 = -10.403124237
x = -10.403124237

Simplifying
x = -10.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.403124237, -10.403124237}
Solution
x = {2.403124237, -10.403124237}

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