(6x+1)(2x+10)=180

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Solution for (6x+1)(2x+10)=180 equation: 


Simplifying
(6x + 1)(2x + 10) = 180

Reorder the terms:
(1 + 6x)(2x + 10) = 180

Reorder the terms:
(1 + 6x)(10 + 2x) = 180

Multiply (1 + 6x) * (10 + 2x)
(1(10 + 2x) + 6x * (10 + 2x)) = 180
((10 * 1 + 2x * 1) + 6x * (10 + 2x)) = 180
((10 + 2x) + 6x * (10 + 2x)) = 180
(10 + 2x + (10 * 6x + 2x * 6x)) = 180
(10 + 2x + (60x + 12x2)) = 180

Combine like terms: 2x + 60x = 62x
(10 + 62x + 12x2) = 180

Solving
10 + 62x + 12x2 = 180

Solving for variable 'x'.

Reorder the terms:
10 + -180 + 62x + 12x2 = 180 + -180

Combine like terms: 10 + -180 = -170
-170 + 62x + 12x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-170 + 62x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-85 + 31x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-85 + 31x + 6x2)' equal to zero and attempt to solve:

Simplifying
-85 + 31x + 6x2 = 0

Solving
-85 + 31x + 6x2 = 0

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

Divide each side by '6'.
-14.16666667 + 5.166666667x + x2 = 0

Move the constant term to the right:

Add '14.16666667' to each side of the equation.
-14.16666667 + 5.166666667x + 14.16666667 + x2 = 0 + 14.16666667

Reorder the terms:
-14.16666667 + 14.16666667 + 5.166666667x + x2 = 0 + 14.16666667

Combine like terms: -14.16666667 + 14.16666667 = 0.00000000
0.00000000 + 5.166666667x + x2 = 0 + 14.16666667
5.166666667x + x2 = 0 + 14.16666667

Combine like terms: 0 + 14.16666667 = 14.16666667
5.166666667x + x2 = 14.16666667

The x term is 5.166666667x.  Take half its coefficient (2.583333334).
Square it (6.673611115) and add it to both sides.

Add '6.673611115' to each side of the equation.
5.166666667x + 6.673611115 + x2 = 14.16666667 + 6.673611115

Reorder the terms:
6.673611115 + 5.166666667x + x2 = 14.16666667 + 6.673611115

Combine like terms: 14.16666667 + 6.673611115 = 20.840277785
6.673611115 + 5.166666667x + x2 = 20.840277785

Factor a perfect square on the left side:
(x + 2.583333334)(x + 2.583333334) = 20.840277785

Calculate the square root of the right side: 4.565115309

Break this problem into two subproblems by setting 
(x + 2.583333334) equal to 4.565115309 and -4.565115309.


Subproblem 1
x + 2.583333334 = 4.565115309

Simplifying
x + 2.583333334 = 4.565115309

Reorder the terms:
2.583333334 + x = 4.565115309

Solving
2.583333334 + x = 4.565115309

Solving for variable 'x'.

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

Add '-2.583333334' to each side of the equation.
2.583333334 + -2.583333334 + x = 4.565115309 + -2.583333334

Combine like terms: 2.583333334 + -2.583333334 = 0.000000000
0.000000000 + x = 4.565115309 + -2.583333334
x = 4.565115309 + -2.583333334

Combine like terms: 4.565115309 + -2.583333334 = 1.981781975
x = 1.981781975

Simplifying
x = 1.981781975


Subproblem 2
x + 2.583333334 = -4.565115309

Simplifying
x + 2.583333334 = -4.565115309

Reorder the terms:
2.583333334 + x = -4.565115309

Solving
2.583333334 + x = -4.565115309

Solving for variable 'x'.

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

Add '-2.583333334' to each side of the equation.
2.583333334 + -2.583333334 + x = -4.565115309 + -2.583333334

Combine like terms: 2.583333334 + -2.583333334 = 0.000000000
0.000000000 + x = -4.565115309 + -2.583333334
x = -4.565115309 + -2.583333334

Combine like terms: -4.565115309 + -2.583333334 = -7.148448643
x = -7.148448643

Simplifying
x = -7.148448643


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.981781975, -7.148448643}
Solution
x = {1.981781975, -7.148448643}

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