H(t)=-4.9t^2+24t

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Solution for H(t)=-4.9t^2+24t equation: 


Simplifying
H(t) = -4.9t2 + 24t

Multiply H * t
tH = -4.9t2 + 24t

Reorder the terms:
tH = 24t + -4.9t2

Solving
tH = 24t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-24t + tH + 4.9t2 = 24t + -4.9t2 + -24t + 4.9t2

Reorder the terms:
-24t + tH + 4.9t2 = 24t + -24t + -4.9t2 + 4.9t2

Combine like terms: 24t + -24t = 0
-24t + tH + 4.9t2 = 0 + -4.9t2 + 4.9t2
-24t + tH + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-24t + tH + 4.9t2 = 0.0

Factor out the Greatest Common Factor (GCF), 't'.
t(-24 + H + 4.9t) = 0.0


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 '(-24 + H + 4.9t)' equal to zero and attempt to solve:

Simplifying
-24 + H + 4.9t = 0

Solving
-24 + H + 4.9t = 0

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

Add '24' to each side of the equation.
-24 + H + 24 + 4.9t = 0 + 24

Reorder the terms:
-24 + 24 + H + 4.9t = 0 + 24

Combine like terms: -24 + 24 = 0
0 + H + 4.9t = 0 + 24
H + 4.9t = 0 + 24

Combine like terms: 0 + 24 = 24
H + 4.9t = 24

Add '-1H' to each side of the equation.
H + -1H + 4.9t = 24 + -1H

Combine like terms: H + -1H = 0
0 + 4.9t = 24 + -1H
4.9t = 24 + -1H

Divide each side by '4.9'.
t = 4.897959184 + -0.2040816327H

Simplifying
t = 4.897959184 + -0.2040816327H
Solution
t = {0, 4.897959184 + -0.2040816327H}

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