S(t)=100t-4.9t^2

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Solution for S(t)=100t-4.9t^2 equation: 


Simplifying
S(t) = 100t + -4.9t2

Multiply S * t
tS = 100t + -4.9t2

Solving
tS = 100t + -4.9t2

Solving for variable 't'.

Reorder the terms:
-100t + tS + 4.9t2 = 100t + -4.9t2 + -100t + 4.9t2

Reorder the terms:
-100t + tS + 4.9t2 = 100t + -100t + -4.9t2 + 4.9t2

Combine like terms: 100t + -100t = 0
-100t + tS + 4.9t2 = 0 + -4.9t2 + 4.9t2
-100t + tS + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-100t + tS + 4.9t2 = 0.0

Factor out the Greatest Common Factor (GCF), 't'.
t(-100 + S + 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 '(-100 + S + 4.9t)' equal to zero and attempt to solve:

Simplifying
-100 + S + 4.9t = 0

Solving
-100 + S + 4.9t = 0

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

Add '100' to each side of the equation.
-100 + S + 100 + 4.9t = 0 + 100

Reorder the terms:
-100 + 100 + S + 4.9t = 0 + 100

Combine like terms: -100 + 100 = 0
0 + S + 4.9t = 0 + 100
S + 4.9t = 0 + 100

Combine like terms: 0 + 100 = 100
S + 4.9t = 100

Add '-1S' to each side of the equation.
S + -1S + 4.9t = 100 + -1S

Combine like terms: S + -1S = 0
0 + 4.9t = 100 + -1S
4.9t = 100 + -1S

Divide each side by '4.9'.
t = 20.40816327 + -0.2040816327S

Simplifying
t = 20.40816327 + -0.2040816327S
Solution
t = {0, 20.40816327 + -0.2040816327S}

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