D(t)=(16t^2)-(120t)

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Solution for D(t)=(16t^2)-(120t) equation: 


Simplifying
D(t) = (16t2) + -1(120t)

Multiply D * t
tD = (16t2) + -1(120t)

Remove parenthesis around (120t)
tD = (16t2) + -1 * 120t

Multiply -1 * 120
tD = (16t2) + -120t

Reorder the terms:
tD = -120t + (16t2)

Solving
tD = -120t + (16t2)

Solving for variable 't'.

Reorder the terms:
120t + tD + (-16t2) = -120t + (16t2) + 120t + (-16t2)

Reorder the terms:
120t + tD + (-16t2) = -120t + 120t + (16t2) + (-16t2)

Combine like terms: -120t + 120t = 0
120t + tD + (-16t2) = 0 + (16t2) + (-16t2)
120t + tD + (-16t2) = (16t2) + (-16t2)

Combine like terms: (16t2) + (-16t2) = 0
120t + tD + (-16t2) = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(120 + D + (-16t)) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(120 + D + (-16t))' equal to zero and attempt to solve:

Simplifying
120 + D + (-16t) = 0

Solving
120 + D + (-16t) = 0

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

Add '-120' to each side of the equation.
120 + D + -120 + (-16t) = 0 + -120

Reorder the terms:
120 + -120 + D + (-16t) = 0 + -120

Combine like terms: 120 + -120 = 0
0 + D + (-16t) = 0 + -120
D + (-16t) = 0 + -120

Combine like terms: 0 + -120 = -120
D + (-16t) = -120

Add '-1D' to each side of the equation.
D + -1D + (-16t) = -120 + -1D

Combine like terms: D + -1D = 0
0 + (-16t) = -120 + -1D
(-16t) = -120 + -1D

Divide each side by '-16'.
t = 7.5 + 0.0625D

Simplifying
t = 7.5 + 0.0625D
Solution
t = {0, 7.5 + 0.0625D}

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