-16x^2+180x+6=0

Solution for -16x^2+180x+6=0 equation:

Simplifying
-16x2 + 180x + 6 = 0

Reorder the terms:
6 + 180x + -16x2 = 0

Solving
6 + 180x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 90x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 90x + -8x2)' equal to zero and attempt to solve:

Simplifying
3 + 90x + -8x2 = 0

Solving
3 + 90x + -8x2 = 0

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

Divide each side by '-8'.
-0.375 + -11.25x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -11.25x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -11.25x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -11.25x + x2 = 0 + 0.375
-11.25x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-11.25x + x2 = 0.375

The x term is -11.25x.  Take half its coefficient (-5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
-11.25x + 31.640625 + x2 = 0.375 + 31.640625

Reorder the terms:
31.640625 + -11.25x + x2 = 0.375 + 31.640625

Combine like terms: 0.375 + 31.640625 = 32.015625
31.640625 + -11.25x + x2 = 32.015625

Factor a perfect square on the left side:
(x + -5.625)(x + -5.625) = 32.015625

Calculate the square root of the right side: 5.658235149

Break this problem into two subproblems by setting 
(x + -5.625) equal to 5.658235149 and -5.658235149.

Subproblem 1
x + -5.625 = 5.658235149

Simplifying
x + -5.625 = 5.658235149

Reorder the terms:
-5.625 + x = 5.658235149

Solving
-5.625 + x = 5.658235149

Solving for variable 'x'.

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

Add '5.625' to each side of the equation.
-5.625 + 5.625 + x = 5.658235149 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + x = 5.658235149 + 5.625
x = 5.658235149 + 5.625

Combine like terms: 5.658235149 + 5.625 = 11.283235149
x = 11.283235149

Simplifying
x = 11.283235149

Subproblem 2
x + -5.625 = -5.658235149

Simplifying
x + -5.625 = -5.658235149

Reorder the terms:
-5.625 + x = -5.658235149

Solving
-5.625 + x = -5.658235149

Solving for variable 'x'.

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

Add '5.625' to each side of the equation.
-5.625 + 5.625 + x = -5.658235149 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + x = -5.658235149 + 5.625
x = -5.658235149 + 5.625

Combine like terms: -5.658235149 + 5.625 = -0.033235149
x = -0.033235149

Simplifying
x = -0.033235149

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.283235149, -0.033235149}
Solution
x = {11.283235149, -0.033235149}