3*x(x+3)=180*180

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Solution for 3*x(x+3)=180*180 equation: 


Simplifying
3x(x + 3) = 180 * 180

Reorder the terms:
3x(3 + x) = 180 * 180
(3 * 3x + x * 3x) = 180 * 180
(9x + 3x2) = 180 * 180

Multiply 180 * 180
9x + 3x2 = 32400

Solving
9x + 3x2 = 32400

Solving for variable 'x'.

Reorder the terms:
-32400 + 9x + 3x2 = 32400 + -32400

Combine like terms: 32400 + -32400 = 0
-32400 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10800 + 3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10800 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-10800 + 3x + x2 = 0

Solving
-10800 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10800' to each side of the equation.
-10800 + 3x + 10800 + x2 = 0 + 10800

Reorder the terms:
-10800 + 10800 + 3x + x2 = 0 + 10800

Combine like terms: -10800 + 10800 = 0
0 + 3x + x2 = 0 + 10800
3x + x2 = 0 + 10800

Combine like terms: 0 + 10800 = 10800
3x + x2 = 10800

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 = 10800 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 10800 + 2.25

Combine like terms: 10800 + 2.25 = 10802.25
2.25 + 3x + x2 = 10802.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10802.25

Calculate the square root of the right side: 103.933873208

Break this problem into two subproblems by setting 
(x + 1.5) equal to 103.933873208 and -103.933873208.


Subproblem 1
x + 1.5 = 103.933873208

Simplifying
x + 1.5 = 103.933873208

Reorder the terms:
1.5 + x = 103.933873208

Solving
1.5 + x = 103.933873208

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 = 103.933873208 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 103.933873208 + -1.5
x = 103.933873208 + -1.5

Combine like terms: 103.933873208 + -1.5 = 102.433873208
x = 102.433873208

Simplifying
x = 102.433873208


Subproblem 2
x + 1.5 = -103.933873208

Simplifying
x + 1.5 = -103.933873208

Reorder the terms:
1.5 + x = -103.933873208

Solving
1.5 + x = -103.933873208

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 = -103.933873208 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -103.933873208 + -1.5
x = -103.933873208 + -1.5

Combine like terms: -103.933873208 + -1.5 = -105.433873208
x = -105.433873208

Simplifying
x = -105.433873208


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {102.433873208, -105.433873208}
Solution
x = {102.433873208, -105.433873208}

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