3(x+3)(x+6)=60

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Solution for 3(x+3)(x+6)=60 equation: 


Simplifying
3(x + 3)(x + 6) = 60

Reorder the terms:
3(3 + x)(x + 6) = 60

Reorder the terms:
3(3 + x)(6 + x) = 60

Multiply (3 + x) * (6 + x)
3(3(6 + x) + x(6 + x)) = 60
3((6 * 3 + x * 3) + x(6 + x)) = 60
3((18 + 3x) + x(6 + x)) = 60
3(18 + 3x + (6 * x + x * x)) = 60
3(18 + 3x + (6x + x2)) = 60

Combine like terms: 3x + 6x = 9x
3(18 + 9x + x2) = 60
(18 * 3 + 9x * 3 + x2 * 3) = 60
(54 + 27x + 3x2) = 60

Solving
54 + 27x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
54 + -60 + 27x + 3x2 = 60 + -60

Combine like terms: 54 + -60 = -6
-6 + 27x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-6 + 27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 9x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + 9x + x2 = 0

Solving
-2 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 9x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 9x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9x + x2 = 0 + 2
9x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
9x + x2 = 2

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 2 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 2 + 20.25

Combine like terms: 2 + 20.25 = 22.25
20.25 + 9x + x2 = 22.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + 4.5 = 4.716990566

Simplifying
x + 4.5 = 4.716990566

Reorder the terms:
4.5 + x = 4.716990566

Solving
4.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.716990566 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.716990566 + -4.5
x = 4.716990566 + -4.5

Combine like terms: 4.716990566 + -4.5 = 0.216990566
x = 0.216990566

Simplifying
x = 0.216990566


Subproblem 2
x + 4.5 = -4.716990566

Simplifying
x + 4.5 = -4.716990566

Reorder the terms:
4.5 + x = -4.716990566

Solving
4.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.716990566 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.716990566 + -4.5
x = -4.716990566 + -4.5

Combine like terms: -4.716990566 + -4.5 = -9.216990566
x = -9.216990566

Simplifying
x = -9.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.216990566, -9.216990566}
Solution
x = {0.216990566, -9.216990566}

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