15x^2-72x-120=0

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Solution for 15x^2-72x-120=0 equation: 


Simplifying
15x2 + -72x + -120 = 0

Reorder the terms:
-120 + -72x + 15x2 = 0

Solving
-120 + -72x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + -24x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + -24x + 5x2)' equal to zero and attempt to solve:

Simplifying
-40 + -24x + 5x2 = 0

Solving
-40 + -24x + 5x2 = 0

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

Divide each side by '5'.
-8 + -4.8x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4.8x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -4.8x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4.8x + x2 = 0 + 8
-4.8x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4.8x + x2 = 8

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = 8 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = 8 + 5.76

Combine like terms: 8 + 5.76 = 13.76
5.76 + -4.8x + x2 = 13.76

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 13.76

Calculate the square root of the right side: 3.709447398

Break this problem into two subproblems by setting 
(x + -2.4) equal to 3.709447398 and -3.709447398.


Subproblem 1
x + -2.4 = 3.709447398

Simplifying
x + -2.4 = 3.709447398

Reorder the terms:
-2.4 + x = 3.709447398

Solving
-2.4 + x = 3.709447398

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = 3.709447398 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = 3.709447398 + 2.4
x = 3.709447398 + 2.4

Combine like terms: 3.709447398 + 2.4 = 6.109447398
x = 6.109447398

Simplifying
x = 6.109447398


Subproblem 2
x + -2.4 = -3.709447398

Simplifying
x + -2.4 = -3.709447398

Reorder the terms:
-2.4 + x = -3.709447398

Solving
-2.4 + x = -3.709447398

Solving for variable 'x'.

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

Add '2.4' to each side of the equation.
-2.4 + 2.4 + x = -3.709447398 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + x = -3.709447398 + 2.4
x = -3.709447398 + 2.4

Combine like terms: -3.709447398 + 2.4 = -1.309447398
x = -1.309447398

Simplifying
x = -1.309447398


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.109447398, -1.309447398}
Solution
x = {6.109447398, -1.309447398}

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