6x^2-39x-60=0

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Solution for 6x^2-39x-60=0 equation: 


Simplifying
6x2 + -39x + -60 = 0

Reorder the terms:
-60 + -39x + 6x2 = 0

Solving
-60 + -39x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -13x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-20 + -13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-20 + -13x + 2x2 = 0

Solving
-20 + -13x + 2x2 = 0

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

Divide each side by '2'.
-10 + -6.5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -6.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -6.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -6.5x + x2 = 0 + 10
-6.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-6.5x + x2 = 10

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 10 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 10 + 10.5625

Combine like terms: 10 + 10.5625 = 20.5625
10.5625 + -6.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.534589287 and -4.534589287.


Subproblem 1
x + -3.25 = 4.534589287

Simplifying
x + -3.25 = 4.534589287

Reorder the terms:
-3.25 + x = 4.534589287

Solving
-3.25 + x = 4.534589287

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 4.534589287 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 4.534589287 + 3.25
x = 4.534589287 + 3.25

Combine like terms: 4.534589287 + 3.25 = 7.784589287
x = 7.784589287

Simplifying
x = 7.784589287


Subproblem 2
x + -3.25 = -4.534589287

Simplifying
x + -3.25 = -4.534589287

Reorder the terms:
-3.25 + x = -4.534589287

Solving
-3.25 + x = -4.534589287

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -4.534589287 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -4.534589287 + 3.25
x = -4.534589287 + 3.25

Combine like terms: -4.534589287 + 3.25 = -1.284589287
x = -1.284589287

Simplifying
x = -1.284589287


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.784589287, -1.284589287}
Solution
x = {7.784589287, -1.284589287}

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