32x^2-24x-48=0

Solution for 32x^2-24x-48=0 equation:

Simplifying
32x2 + -24x + -48 = 0

Reorder the terms:
-48 + -24x + 32x2 = 0

Solving
-48 + -24x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-6 + -3x + 4x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-6 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-6 + -3x + 4x2 = 0

Solving
-6 + -3x + 4x2 = 0

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

Divide each side by '4'.
-1.5 + -0.75x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -0.75x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -0.75x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -0.75x + x2 = 0 + 1.5
-0.75x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-0.75x + x2 = 1.5

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.5 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.5 + 0.140625

Combine like terms: 1.5 + 0.140625 = 1.640625
0.140625 + -0.75x + x2 = 1.640625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.280868846 and -1.280868846.

Subproblem 1
x + -0.375 = 1.280868846

Simplifying
x + -0.375 = 1.280868846

Reorder the terms:
-0.375 + x = 1.280868846

Solving
-0.375 + x = 1.280868846

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.280868846 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.280868846 + 0.375
x = 1.280868846 + 0.375

Combine like terms: 1.280868846 + 0.375 = 1.655868846
x = 1.655868846

Simplifying
x = 1.655868846

Subproblem 2
x + -0.375 = -1.280868846

Simplifying
x + -0.375 = -1.280868846

Reorder the terms:
-0.375 + x = -1.280868846

Solving
-0.375 + x = -1.280868846

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.280868846 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.280868846 + 0.375
x = -1.280868846 + 0.375

Combine like terms: -1.280868846 + 0.375 = -0.905868846
x = -0.905868846

Simplifying
x = -0.905868846

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.655868846, -0.905868846}
Solution
x = {1.655868846, -0.905868846}