(300+x)(1500+9x)=6

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Solution for (300+x)(1500+9x)=6 equation: 


Simplifying
(300 + x)(1500 + 9x) = 6

Multiply (300 + x) * (1500 + 9x)
(300(1500 + 9x) + x(1500 + 9x)) = 6
((1500 * 300 + 9x * 300) + x(1500 + 9x)) = 6
((450000 + 2700x) + x(1500 + 9x)) = 6
(450000 + 2700x + (1500 * x + 9x * x)) = 6
(450000 + 2700x + (1500x + 9x2)) = 6

Combine like terms: 2700x + 1500x = 4200x
(450000 + 4200x + 9x2) = 6

Solving
450000 + 4200x + 9x2 = 6

Solving for variable 'x'.

Reorder the terms:
450000 + -6 + 4200x + 9x2 = 6 + -6

Combine like terms: 450000 + -6 = 449994
449994 + 4200x + 9x2 = 6 + -6

Combine like terms: 6 + -6 = 0
449994 + 4200x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(149998 + 1400x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(149998 + 1400x + 3x2)' equal to zero and attempt to solve:

Simplifying
149998 + 1400x + 3x2 = 0

Solving
149998 + 1400x + 3x2 = 0

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

Divide each side by '3'.
49999.33333 + 466.6666667x + x2 = 0

Move the constant term to the right:

Add '-49999.33333' to each side of the equation.
49999.33333 + 466.6666667x + -49999.33333 + x2 = 0 + -49999.33333

Reorder the terms:
49999.33333 + -49999.33333 + 466.6666667x + x2 = 0 + -49999.33333

Combine like terms: 49999.33333 + -49999.33333 = 0.00000
0.00000 + 466.6666667x + x2 = 0 + -49999.33333
466.6666667x + x2 = 0 + -49999.33333

Combine like terms: 0 + -49999.33333 = -49999.33333
466.6666667x + x2 = -49999.33333

The x term is 466.6666667x.  Take half its coefficient (233.3333334).
Square it (54444.44448) and add it to both sides.

Add '54444.44448' to each side of the equation.
466.6666667x + 54444.44448 + x2 = -49999.33333 + 54444.44448

Reorder the terms:
54444.44448 + 466.6666667x + x2 = -49999.33333 + 54444.44448

Combine like terms: -49999.33333 + 54444.44448 = 4445.11115
54444.44448 + 466.6666667x + x2 = 4445.11115

Factor a perfect square on the left side:
(x + 233.3333334)(x + 233.3333334) = 4445.11115

Calculate the square root of the right side: 66.671666771

Break this problem into two subproblems by setting 
(x + 233.3333334) equal to 66.671666771 and -66.671666771.


Subproblem 1
x + 233.3333334 = 66.671666771

Simplifying
x + 233.3333334 = 66.671666771

Reorder the terms:
233.3333334 + x = 66.671666771

Solving
233.3333334 + x = 66.671666771

Solving for variable 'x'.

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

Add '-233.3333334' to each side of the equation.
233.3333334 + -233.3333334 + x = 66.671666771 + -233.3333334

Combine like terms: 233.3333334 + -233.3333334 = 0.0000000
0.0000000 + x = 66.671666771 + -233.3333334
x = 66.671666771 + -233.3333334

Combine like terms: 66.671666771 + -233.3333334 = -166.661666629
x = -166.661666629

Simplifying
x = -166.661666629


Subproblem 2
x + 233.3333334 = -66.671666771

Simplifying
x + 233.3333334 = -66.671666771

Reorder the terms:
233.3333334 + x = -66.671666771

Solving
233.3333334 + x = -66.671666771

Solving for variable 'x'.

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

Add '-233.3333334' to each side of the equation.
233.3333334 + -233.3333334 + x = -66.671666771 + -233.3333334

Combine like terms: 233.3333334 + -233.3333334 = 0.0000000
0.0000000 + x = -66.671666771 + -233.3333334
x = -66.671666771 + -233.3333334

Combine like terms: -66.671666771 + -233.3333334 = -300.005000171
x = -300.005000171

Simplifying
x = -300.005000171


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-166.661666629, -300.005000171}
Solution
x = {-166.661666629, -300.005000171}

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