-16x^2+150x+120=0

Solution for -16x^2+150x+120=0 equation:

Simplifying
-16x2 + 150x + 120 = 0

Reorder the terms:
120 + 150x + -16x2 = 0

Solving
120 + 150x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(60 + 75x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(60 + 75x + -8x2)' equal to zero and attempt to solve:

Simplifying
60 + 75x + -8x2 = 0

Solving
60 + 75x + -8x2 = 0

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

Divide each side by '-8'.
-7.5 + -9.375x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -9.375x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -9.375x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -9.375x + x2 = 0 + 7.5
-9.375x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-9.375x + x2 = 7.5

The x term is -9.375x.  Take half its coefficient (-4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
-9.375x + 21.97265625 + x2 = 7.5 + 21.97265625

Reorder the terms:
21.97265625 + -9.375x + x2 = 7.5 + 21.97265625

Combine like terms: 7.5 + 21.97265625 = 29.47265625
21.97265625 + -9.375x + x2 = 29.47265625

Factor a perfect square on the left side:
(x + -4.6875)(x + -4.6875) = 29.47265625

Calculate the square root of the right side: 5.428872466

Break this problem into two subproblems by setting 
(x + -4.6875) equal to 5.428872466 and -5.428872466.

Subproblem 1
x + -4.6875 = 5.428872466

Simplifying
x + -4.6875 = 5.428872466

Reorder the terms:
-4.6875 + x = 5.428872466

Solving
-4.6875 + x = 5.428872466

Solving for variable 'x'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + x = 5.428872466 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + x = 5.428872466 + 4.6875
x = 5.428872466 + 4.6875

Combine like terms: 5.428872466 + 4.6875 = 10.116372466
x = 10.116372466

Simplifying
x = 10.116372466

Subproblem 2
x + -4.6875 = -5.428872466

Simplifying
x + -4.6875 = -5.428872466

Reorder the terms:
-4.6875 + x = -5.428872466

Solving
-4.6875 + x = -5.428872466

Solving for variable 'x'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + x = -5.428872466 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + x = -5.428872466 + 4.6875
x = -5.428872466 + 4.6875

Combine like terms: -5.428872466 + 4.6875 = -0.741372466
x = -0.741372466

Simplifying
x = -0.741372466

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.116372466, -0.741372466}
Solution
x = {10.116372466, -0.741372466}