-16x^2+24x+6=0

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Solution for -16x^2+24x+6=0 equation: 


Simplifying
-16x2 + 24x + 6 = 0

Reorder the terms:
6 + 24x + -16x2 = 0

Solving
6 + 24x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 12x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + 12x + -8x2)' equal to zero and attempt to solve:

Simplifying
3 + 12x + -8x2 = 0

Solving
3 + 12x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.375 + -1.5x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -1.5x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -1.5x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -1.5x + x2 = 0 + 0.375
-1.5x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-1.5x + x2 = 0.375

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 0.375 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 0.375 + 0.5625

Combine like terms: 0.375 + 0.5625 = 0.9375
0.5625 + -1.5x + x2 = 0.9375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.968245837 and -0.968245837.


Subproblem 1
x + -0.75 = 0.968245837

Simplifying
x + -0.75 = 0.968245837

Reorder the terms:
-0.75 + x = 0.968245837

Solving
-0.75 + x = 0.968245837

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.968245837 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.968245837 + 0.75
x = 0.968245837 + 0.75

Combine like terms: 0.968245837 + 0.75 = 1.718245837
x = 1.718245837

Simplifying
x = 1.718245837


Subproblem 2
x + -0.75 = -0.968245837

Simplifying
x + -0.75 = -0.968245837

Reorder the terms:
-0.75 + x = -0.968245837

Solving
-0.75 + x = -0.968245837

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.968245837 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.968245837 + 0.75
x = -0.968245837 + 0.75

Combine like terms: -0.968245837 + 0.75 = -0.218245837
x = -0.218245837

Simplifying
x = -0.218245837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.718245837, -0.218245837}
Solution
x = {1.718245837, -0.218245837}

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