15x^2-110x-60=0

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Solution for 15x^2-110x-60=0 equation: 


Simplifying
15x2 + -110x + -60 = 0

Reorder the terms:
-60 + -110x + 15x2 = 0

Solving
-60 + -110x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -22x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-12 + -22x + 3x2)' equal to zero and attempt to solve:

Simplifying
-12 + -22x + 3x2 = 0

Solving
-12 + -22x + 3x2 = 0

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

Divide each side by '3'.
-4 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -7.333333333x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -7.333333333x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7.333333333x + x2 = 0 + 4
-7.333333333x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-7.333333333x + x2 = 4

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 4 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 4 + 13.44444445

Combine like terms: 4 + 13.44444445 = 17.44444445
13.44444445 + -7.333333333x + x2 = 17.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 17.44444445

Calculate the square root of the right side: 4.176654696

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 4.176654696 and -4.176654696.


Subproblem 1
x + -3.666666667 = 4.176654696

Simplifying
x + -3.666666667 = 4.176654696

Reorder the terms:
-3.666666667 + x = 4.176654696

Solving
-3.666666667 + x = 4.176654696

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 4.176654696 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 4.176654696 + 3.666666667
x = 4.176654696 + 3.666666667

Combine like terms: 4.176654696 + 3.666666667 = 7.843321363
x = 7.843321363

Simplifying
x = 7.843321363


Subproblem 2
x + -3.666666667 = -4.176654696

Simplifying
x + -3.666666667 = -4.176654696

Reorder the terms:
-3.666666667 + x = -4.176654696

Solving
-3.666666667 + x = -4.176654696

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -4.176654696 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -4.176654696 + 3.666666667
x = -4.176654696 + 3.666666667

Combine like terms: -4.176654696 + 3.666666667 = -0.509988029
x = -0.509988029

Simplifying
x = -0.509988029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.843321363, -0.509988029}
Solution
x = {7.843321363, -0.509988029}

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