9x(x-2)=147

Solution for 9x(x-2)=147 equation:

Simplifying
9x(x + -2) = 147

Reorder the terms:
9x(-2 + x) = 147
(-2 * 9x + x * 9x) = 147
(-18x + 9x2) = 147

Solving
-18x + 9x2 = 147

Solving for variable 'x'.

Reorder the terms:
-147 + -18x + 9x2 = 147 + -147

Combine like terms: 147 + -147 = 0
-147 + -18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-49 + -6x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-49 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-49 + -6x + 3x2 = 0

Solving
-49 + -6x + 3x2 = 0

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

Divide each side by '3'.
-16.33333333 + -2x + x2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + -2x + 16.33333333 + x2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + -2x + x2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + -2x + x2 = 0 + 16.33333333
-2x + x2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
-2x + x2 = 16.33333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 16.33333333 + 1

Reorder the terms:
1 + -2x + x2 = 16.33333333 + 1

Combine like terms: 16.33333333 + 1 = 17.33333333
1 + -2x + x2 = 17.33333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 17.33333333

Calculate the square root of the right side: 4.163331999

Break this problem into two subproblems by setting 
(x + -1) equal to 4.163331999 and -4.163331999.

Subproblem 1
x + -1 = 4.163331999

Simplifying
x + -1 = 4.163331999

Reorder the terms:
-1 + x = 4.163331999

Solving
-1 + x = 4.163331999

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.163331999 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.163331999 + 1
x = 4.163331999 + 1

Combine like terms: 4.163331999 + 1 = 5.163331999
x = 5.163331999

Simplifying
x = 5.163331999

Subproblem 2
x + -1 = -4.163331999

Simplifying
x + -1 = -4.163331999

Reorder the terms:
-1 + x = -4.163331999

Solving
-1 + x = -4.163331999

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.163331999 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.163331999 + 1
x = -4.163331999 + 1

Combine like terms: -4.163331999 + 1 = -3.163331999
x = -3.163331999

Simplifying
x = -3.163331999

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.163331999, -3.163331999}
Solution
x = {5.163331999, -3.163331999}