(3x+100)(6x-10)=180

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Solution for (3x+100)(6x-10)=180 equation: 


Simplifying
(3x + 100)(6x + -10) = 180

Reorder the terms:
(100 + 3x)(6x + -10) = 180

Reorder the terms:
(100 + 3x)(-10 + 6x) = 180

Multiply (100 + 3x) * (-10 + 6x)
(100(-10 + 6x) + 3x * (-10 + 6x)) = 180
((-10 * 100 + 6x * 100) + 3x * (-10 + 6x)) = 180
((-1000 + 600x) + 3x * (-10 + 6x)) = 180
(-1000 + 600x + (-10 * 3x + 6x * 3x)) = 180
(-1000 + 600x + (-30x + 18x2)) = 180

Combine like terms: 600x + -30x = 570x
(-1000 + 570x + 18x2) = 180

Solving
-1000 + 570x + 18x2 = 180

Solving for variable 'x'.

Reorder the terms:
-1000 + -180 + 570x + 18x2 = 180 + -180

Combine like terms: -1000 + -180 = -1180
-1180 + 570x + 18x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-1180 + 570x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-590 + 285x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-590 + 285x + 9x2)' equal to zero and attempt to solve:

Simplifying
-590 + 285x + 9x2 = 0

Solving
-590 + 285x + 9x2 = 0

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

Divide each side by '9'.
-65.55555556 + 31.66666667x + x2 = 0

Move the constant term to the right:

Add '65.55555556' to each side of the equation.
-65.55555556 + 31.66666667x + 65.55555556 + x2 = 0 + 65.55555556

Reorder the terms:
-65.55555556 + 65.55555556 + 31.66666667x + x2 = 0 + 65.55555556

Combine like terms: -65.55555556 + 65.55555556 = 0.00000000
0.00000000 + 31.66666667x + x2 = 0 + 65.55555556
31.66666667x + x2 = 0 + 65.55555556

Combine like terms: 0 + 65.55555556 = 65.55555556
31.66666667x + x2 = 65.55555556

The x term is 31.66666667x.  Take half its coefficient (15.83333334).
Square it (250.6944447) and add it to both sides.

Add '250.6944447' to each side of the equation.
31.66666667x + 250.6944447 + x2 = 65.55555556 + 250.6944447

Reorder the terms:
250.6944447 + 31.66666667x + x2 = 65.55555556 + 250.6944447

Combine like terms: 65.55555556 + 250.6944447 = 316.25000026
250.6944447 + 31.66666667x + x2 = 316.25000026

Factor a perfect square on the left side:
(x + 15.83333334)(x + 15.83333334) = 316.25000026

Calculate the square root of the right side: 17.783419251

Break this problem into two subproblems by setting 
(x + 15.83333334) equal to 17.783419251 and -17.783419251.


Subproblem 1
x + 15.83333334 = 17.783419251

Simplifying
x + 15.83333334 = 17.783419251

Reorder the terms:
15.83333334 + x = 17.783419251

Solving
15.83333334 + x = 17.783419251

Solving for variable 'x'.

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

Add '-15.83333334' to each side of the equation.
15.83333334 + -15.83333334 + x = 17.783419251 + -15.83333334

Combine like terms: 15.83333334 + -15.83333334 = 0.00000000
0.00000000 + x = 17.783419251 + -15.83333334
x = 17.783419251 + -15.83333334

Combine like terms: 17.783419251 + -15.83333334 = 1.950085911
x = 1.950085911

Simplifying
x = 1.950085911


Subproblem 2
x + 15.83333334 = -17.783419251

Simplifying
x + 15.83333334 = -17.783419251

Reorder the terms:
15.83333334 + x = -17.783419251

Solving
15.83333334 + x = -17.783419251

Solving for variable 'x'.

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

Add '-15.83333334' to each side of the equation.
15.83333334 + -15.83333334 + x = -17.783419251 + -15.83333334

Combine like terms: 15.83333334 + -15.83333334 = 0.00000000
0.00000000 + x = -17.783419251 + -15.83333334
x = -17.783419251 + -15.83333334

Combine like terms: -17.783419251 + -15.83333334 = -33.616752591
x = -33.616752591

Simplifying
x = -33.616752591


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.950085911, -33.616752591}
Solution
x = {1.950085911, -33.616752591}

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