9x-3x(x-5)=6x+3

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Solution for 9x-3x(x-5)=6x+3 equation: 


Simplifying
9x + -3x(x + -5) = 6x + 3

Reorder the terms:
9x + -3x(-5 + x) = 6x + 3
9x + (-5 * -3x + x * -3x) = 6x + 3
9x + (15x + -3x2) = 6x + 3

Combine like terms: 9x + 15x = 24x
24x + -3x2 = 6x + 3

Reorder the terms:
24x + -3x2 = 3 + 6x

Solving
24x + -3x2 = 3 + 6x

Solving for variable 'x'.

Reorder the terms:
-3 + 24x + -6x + -3x2 = 3 + 6x + -3 + -6x

Combine like terms: 24x + -6x = 18x
-3 + 18x + -3x2 = 3 + 6x + -3 + -6x

Reorder the terms:
-3 + 18x + -3x2 = 3 + -3 + 6x + -6x

Combine like terms: 3 + -3 = 0
-3 + 18x + -3x2 = 0 + 6x + -6x
-3 + 18x + -3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-3 + 18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 6x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + 6x + -1x2 = 0

Solving
-1 + 6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -6x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -6x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x + x2 = 0 + -1
-6x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6x + x2 = -1

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1 + 9

Reorder the terms:
9 + -6x + x2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + -6x + x2 = 8

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -3) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -3 = 2.828427125

Simplifying
x + -3 = 2.828427125

Reorder the terms:
-3 + x = 2.828427125

Solving
-3 + x = 2.828427125

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.828427125 + 3
x = 2.828427125 + 3

Combine like terms: 2.828427125 + 3 = 5.828427125
x = 5.828427125

Simplifying
x = 5.828427125


Subproblem 2
x + -3 = -2.828427125

Simplifying
x + -3 = -2.828427125

Reorder the terms:
-3 + x = -2.828427125

Solving
-3 + x = -2.828427125

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.828427125 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.828427125 + 3
x = -2.828427125 + 3

Combine like terms: -2.828427125 + 3 = 0.171572875
x = 0.171572875

Simplifying
x = 0.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.828427125, 0.171572875}
Solution
x = {5.828427125, 0.171572875}

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