15x^2-12x-48=0

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Solution for 15x^2-12x-48=0 equation: 


Simplifying
15x2 + -12x + -48 = 0

Reorder the terms:
-48 + -12x + 15x2 = 0

Solving
-48 + -12x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + -4x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + -4x + 5x2)' equal to zero and attempt to solve:

Simplifying
-16 + -4x + 5x2 = 0

Solving
-16 + -4x + 5x2 = 0

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

Divide each side by '5'.
-3.2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -0.8x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -0.8x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -0.8x + x2 = 0 + 3.2
-0.8x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-0.8x + x2 = 3.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 3.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 3.2 + 0.16

Combine like terms: 3.2 + 0.16 = 3.36
0.16 + -0.8x + x2 = 3.36

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.833030278 and -1.833030278.


Subproblem 1
x + -0.4 = 1.833030278

Simplifying
x + -0.4 = 1.833030278

Reorder the terms:
-0.4 + x = 1.833030278

Solving
-0.4 + x = 1.833030278

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 1.833030278 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 1.833030278 + 0.4
x = 1.833030278 + 0.4

Combine like terms: 1.833030278 + 0.4 = 2.233030278
x = 2.233030278

Simplifying
x = 2.233030278


Subproblem 2
x + -0.4 = -1.833030278

Simplifying
x + -0.4 = -1.833030278

Reorder the terms:
-0.4 + x = -1.833030278

Solving
-0.4 + x = -1.833030278

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -1.833030278 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -1.833030278 + 0.4
x = -1.833030278 + 0.4

Combine like terms: -1.833030278 + 0.4 = -1.433030278
x = -1.433030278

Simplifying
x = -1.433030278


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.233030278, -1.433030278}
Solution
x = {2.233030278, -1.433030278}

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