-16x^2+30x+6=0

Solution for -16x^2+30x+6=0 equation:

Simplifying
-16x2 + 30x + 6 = 0

Reorder the terms:
6 + 30x + -16x2 = 0

Solving
6 + 30x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 15x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 15x + -8x2)' equal to zero and attempt to solve:

Simplifying
3 + 15x + -8x2 = 0

Solving
3 + 15x + -8x2 = 0

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

Divide each side by '-8'.
-0.375 + -1.875x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -1.875x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -1.875x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -1.875x + x2 = 0 + 0.375
-1.875x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-1.875x + x2 = 0.375

The x term is -1.875x.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875x + 0.87890625 + x2 = 0.375 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = 0.375 + 0.87890625

Combine like terms: 0.375 + 0.87890625 = 1.25390625
0.87890625 + -1.875x + x2 = 1.25390625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 1.25390625

Calculate the square root of the right side: 1.119779554

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 1.119779554 and -1.119779554.

Subproblem 1
x + -0.9375 = 1.119779554

Simplifying
x + -0.9375 = 1.119779554

Reorder the terms:
-0.9375 + x = 1.119779554

Solving
-0.9375 + x = 1.119779554

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = 1.119779554 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = 1.119779554 + 0.9375
x = 1.119779554 + 0.9375

Combine like terms: 1.119779554 + 0.9375 = 2.057279554
x = 2.057279554

Simplifying
x = 2.057279554

Subproblem 2
x + -0.9375 = -1.119779554

Simplifying
x + -0.9375 = -1.119779554

Reorder the terms:
-0.9375 + x = -1.119779554

Solving
-0.9375 + x = -1.119779554

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = -1.119779554 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = -1.119779554 + 0.9375
x = -1.119779554 + 0.9375

Combine like terms: -1.119779554 + 0.9375 = -0.182279554
x = -0.182279554

Simplifying
x = -0.182279554

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.057279554, -0.182279554}
Solution
x = {2.057279554, -0.182279554}