-16x^2+21x-6=0

Solution for -16x^2+21x-6=0 equation:

Simplifying
-16x2 + 21x + -6 = 0

Reorder the terms:
-6 + 21x + -16x2 = 0

Solving
-6 + 21x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.375 + -1.3125x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.3125x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.3125x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.3125x + x2 = 0 + -0.375
-1.3125x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.3125x + x2 = -0.375

The x term is -1.3125x.  Take half its coefficient (-0.65625).
Square it (0.4306640625) and add it to both sides.

Add '0.4306640625' to each side of the equation.
-1.3125x + 0.4306640625 + x2 = -0.375 + 0.4306640625

Reorder the terms:
0.4306640625 + -1.3125x + x2 = -0.375 + 0.4306640625

Combine like terms: -0.375 + 0.4306640625 = 0.0556640625
0.4306640625 + -1.3125x + x2 = 0.0556640625

Factor a perfect square on the left side:
(x + -0.65625)(x + -0.65625) = 0.0556640625

Calculate the square root of the right side: 0.235932326

Break this problem into two subproblems by setting 
(x + -0.65625) equal to 0.235932326 and -0.235932326.

Subproblem 1
x + -0.65625 = 0.235932326

Simplifying
x + -0.65625 = 0.235932326

Reorder the terms:
-0.65625 + x = 0.235932326

Solving
-0.65625 + x = 0.235932326

Solving for variable 'x'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + x = 0.235932326 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + x = 0.235932326 + 0.65625
x = 0.235932326 + 0.65625

Combine like terms: 0.235932326 + 0.65625 = 0.892182326
x = 0.892182326

Simplifying
x = 0.892182326

Subproblem 2
x + -0.65625 = -0.235932326

Simplifying
x + -0.65625 = -0.235932326

Reorder the terms:
-0.65625 + x = -0.235932326

Solving
-0.65625 + x = -0.235932326

Solving for variable 'x'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + x = -0.235932326 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + x = -0.235932326 + 0.65625
x = -0.235932326 + 0.65625

Combine like terms: -0.235932326 + 0.65625 = 0.420317674
x = 0.420317674

Simplifying
x = 0.420317674

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.892182326, 0.420317674}