(3x-9)x=5760

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Solution for (3x-9)x=5760 equation: 


Simplifying
(3x + -9) * x = 5760

Reorder the terms:
(-9 + 3x) * x = 5760

Reorder the terms for easier multiplication:
x(-9 + 3x) = 5760
(-9 * x + 3x * x) = 5760
(-9x + 3x2) = 5760

Solving
-9x + 3x2 = 5760

Solving for variable 'x'.

Reorder the terms:
-5760 + -9x + 3x2 = 5760 + -5760

Combine like terms: 5760 + -5760 = 0
-5760 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1920 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1920 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-1920 + -3x + x2 = 0

Solving
-1920 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1920' to each side of the equation.
-1920 + -3x + 1920 + x2 = 0 + 1920

Reorder the terms:
-1920 + 1920 + -3x + x2 = 0 + 1920

Combine like terms: -1920 + 1920 = 0
0 + -3x + x2 = 0 + 1920
-3x + x2 = 0 + 1920

Combine like terms: 0 + 1920 = 1920
-3x + x2 = 1920

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 = 1920 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1920 + 2.25

Combine like terms: 1920 + 2.25 = 1922.25
2.25 + -3x + x2 = 1922.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1922.25

Calculate the square root of the right side: 43.843471578

Break this problem into two subproblems by setting 
(x + -1.5) equal to 43.843471578 and -43.843471578.


Subproblem 1
x + -1.5 = 43.843471578

Simplifying
x + -1.5 = 43.843471578

Reorder the terms:
-1.5 + x = 43.843471578

Solving
-1.5 + x = 43.843471578

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 = 43.843471578 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 43.843471578 + 1.5
x = 43.843471578 + 1.5

Combine like terms: 43.843471578 + 1.5 = 45.343471578
x = 45.343471578

Simplifying
x = 45.343471578


Subproblem 2
x + -1.5 = -43.843471578

Simplifying
x + -1.5 = -43.843471578

Reorder the terms:
-1.5 + x = -43.843471578

Solving
-1.5 + x = -43.843471578

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 = -43.843471578 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -43.843471578 + 1.5
x = -43.843471578 + 1.5

Combine like terms: -43.843471578 + 1.5 = -42.343471578
x = -42.343471578

Simplifying
x = -42.343471578


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.343471578, -42.343471578}
Solution
x = {45.343471578, -42.343471578}

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