15x^2-100x-60=0

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Solution for 15x^2-100x-60=0 equation: 


Simplifying
15x2 + -100x + -60 = 0

Reorder the terms:
-60 + -100x + 15x2 = 0

Solving
-60 + -100x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -20x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-12 + -20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-12 + -20x + 3x2 = 0

Solving
-12 + -20x + 3x2 = 0

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

Divide each side by '3'.
-4 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6.666666667x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -6.666666667x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6.666666667x + x2 = 0 + 4
-6.666666667x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6.666666667x + x2 = 4

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 4 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 4 + 11.11111112

Combine like terms: 4 + 11.11111112 = 15.11111112
11.11111112 + -6.666666667x + x2 = 15.11111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 15.11111112

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.887301264 and -3.887301264.


Subproblem 1
x + -3.333333334 = 3.887301264

Simplifying
x + -3.333333334 = 3.887301264

Reorder the terms:
-3.333333334 + x = 3.887301264

Solving
-3.333333334 + x = 3.887301264

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.887301264 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.887301264 + 3.333333334
x = 3.887301264 + 3.333333334

Combine like terms: 3.887301264 + 3.333333334 = 7.220634598
x = 7.220634598

Simplifying
x = 7.220634598


Subproblem 2
x + -3.333333334 = -3.887301264

Simplifying
x + -3.333333334 = -3.887301264

Reorder the terms:
-3.333333334 + x = -3.887301264

Solving
-3.333333334 + x = -3.887301264

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.887301264 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.887301264 + 3.333333334
x = -3.887301264 + 3.333333334

Combine like terms: -3.887301264 + 3.333333334 = -0.55396793
x = -0.55396793

Simplifying
x = -0.55396793


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.220634598, -0.55396793}
Solution
x = {7.220634598, -0.55396793}

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