240=-16t^2+120t

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


Simplifying
240 = -16t2 + 120t

Reorder the terms:
240 = 120t + -16t2

Solving
240 = 120t + -16t2

Solving for variable 't'.

Reorder the terms:
240 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2

Combine like terms: 120t + -120t = 0
240 + -120t + 16t2 = 0 + -16t2 + 16t2
240 + -120t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
240 + -120t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(30 + -15t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(30 + -15t + 2t2)' equal to zero and attempt to solve:

Simplifying
30 + -15t + 2t2 = 0

Solving
30 + -15t + 2t2 = 0

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

Divide each side by '2'.
15 + -7.5t + t2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -7.5t + -15 + t2 = 0 + -15

Reorder the terms:
15 + -15 + -7.5t + t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7.5t + t2 = 0 + -15
-7.5t + t2 = 0 + -15

Combine like terms: 0 + -15 = -15
-7.5t + t2 = -15

The t term is -7.5t.  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.
-7.5t + 14.0625 + t2 = -15 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = -15 + 14.0625

Combine like terms: -15 + 14.0625 = -0.9375
14.0625 + -7.5t + t2 = -0.9375

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = -0.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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