-16x^2+120x+240=0

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Solution for -16x^2+120x+240=0 equation: 


Simplifying
-16x2 + 120x + 240 = 0

Reorder the terms:
240 + 120x + -16x2 = 0

Solving
240 + 120x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(30 + 15x + -2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(30 + 15x + -2x2)' equal to zero and attempt to solve:

Simplifying
30 + 15x + -2x2 = 0

Solving
30 + 15x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-15 + -7.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -7.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -7.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -7.5x + x2 = 0 + 15
-7.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-7.5x + x2 = 15

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 15 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 15 + 14.0625

Combine like terms: 15 + 14.0625 = 29.0625
14.0625 + -7.5x + x2 = 29.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 29.0625

Calculate the square root of the right side: 5.390964663

Break this problem into two subproblems by setting 
(x + -3.75) equal to 5.390964663 and -5.390964663.


Subproblem 1
x + -3.75 = 5.390964663

Simplifying
x + -3.75 = 5.390964663

Reorder the terms:
-3.75 + x = 5.390964663

Solving
-3.75 + x = 5.390964663

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 5.390964663 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 5.390964663 + 3.75
x = 5.390964663 + 3.75

Combine like terms: 5.390964663 + 3.75 = 9.140964663
x = 9.140964663

Simplifying
x = 9.140964663


Subproblem 2
x + -3.75 = -5.390964663

Simplifying
x + -3.75 = -5.390964663

Reorder the terms:
-3.75 + x = -5.390964663

Solving
-3.75 + x = -5.390964663

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -5.390964663 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -5.390964663 + 3.75
x = -5.390964663 + 3.75

Combine like terms: -5.390964663 + 3.75 = -1.640964663
x = -1.640964663

Simplifying
x = -1.640964663


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.140964663, -1.640964663}
Solution
x = {9.140964663, -1.640964663}

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