3x(4x+18)=360

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Solution for 3x(4x+18)=360 equation: 


Simplifying
3x(4x + 18) = 360

Reorder the terms:
3x(18 + 4x) = 360
(18 * 3x + 4x * 3x) = 360
(54x + 12x2) = 360

Solving
54x + 12x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 54x + 12x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 54x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-60 + 9x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-60 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
-60 + 9x + 2x2 = 0

Solving
-60 + 9x + 2x2 = 0

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

Divide each side by '2'.
-30 + 4.5x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4.5x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 4.5x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4.5x + x2 = 0 + 30
4.5x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
4.5x + x2 = 30

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 30 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 30 + 5.0625

Combine like terms: 30 + 5.0625 = 35.0625
5.0625 + 4.5x + x2 = 35.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(x + 2.25) equal to 5.921359641 and -5.921359641.


Subproblem 1
x + 2.25 = 5.921359641

Simplifying
x + 2.25 = 5.921359641

Reorder the terms:
2.25 + x = 5.921359641

Solving
2.25 + x = 5.921359641

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 5.921359641 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 5.921359641 + -2.25
x = 5.921359641 + -2.25

Combine like terms: 5.921359641 + -2.25 = 3.671359641
x = 3.671359641

Simplifying
x = 3.671359641


Subproblem 2
x + 2.25 = -5.921359641

Simplifying
x + 2.25 = -5.921359641

Reorder the terms:
2.25 + x = -5.921359641

Solving
2.25 + x = -5.921359641

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -5.921359641 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -5.921359641 + -2.25
x = -5.921359641 + -2.25

Combine like terms: -5.921359641 + -2.25 = -8.171359641
x = -8.171359641

Simplifying
x = -8.171359641


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.671359641, -8.171359641}
Solution
x = {3.671359641, -8.171359641}

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