9x(3x-15)=45

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Solution for 9x(3x-15)=45 equation: 


Simplifying
9x(3x + -15) = 45

Reorder the terms:
9x(-15 + 3x) = 45
(-15 * 9x + 3x * 9x) = 45
(-135x + 27x2) = 45

Solving
-135x + 27x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -135x + 27x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -135x + 27x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-5 + -15x + 3x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-5 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + -15x + 3x2 = 0

Solving
-5 + -15x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -5x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -5x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + 1.666666667
-5x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-5x + x2 = 1.666666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 1.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 1.666666667 + 6.25

Combine like terms: 1.666666667 + 6.25 = 7.916666667
6.25 + -5x + x2 = 7.916666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 7.916666667

Calculate the square root of the right side: 2.813657169

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.813657169 and -2.813657169.


Subproblem 1
x + -2.5 = 2.813657169

Simplifying
x + -2.5 = 2.813657169

Reorder the terms:
-2.5 + x = 2.813657169

Solving
-2.5 + x = 2.813657169

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.813657169 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.813657169 + 2.5
x = 2.813657169 + 2.5

Combine like terms: 2.813657169 + 2.5 = 5.313657169
x = 5.313657169

Simplifying
x = 5.313657169


Subproblem 2
x + -2.5 = -2.813657169

Simplifying
x + -2.5 = -2.813657169

Reorder the terms:
-2.5 + x = -2.813657169

Solving
-2.5 + x = -2.813657169

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.813657169 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.813657169 + 2.5
x = -2.813657169 + 2.5

Combine like terms: -2.813657169 + 2.5 = -0.313657169
x = -0.313657169

Simplifying
x = -0.313657169


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.313657169, -0.313657169}
Solution
x = {5.313657169, -0.313657169}

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