v(t)=50t+30t^2

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Solution for v(t)=50t+30t^2 equation: 


Simplifying
v(t) = 50t + 30t2

Multiply v * t
tv = 50t + 30t2

Solving
tv = 50t + 30t2

Solving for variable 't'.

Reorder the terms:
-50t + tv + -30t2 = 50t + 30t2 + -50t + -30t2

Reorder the terms:
-50t + tv + -30t2 = 50t + -50t + 30t2 + -30t2

Combine like terms: 50t + -50t = 0
-50t + tv + -30t2 = 0 + 30t2 + -30t2
-50t + tv + -30t2 = 30t2 + -30t2

Combine like terms: 30t2 + -30t2 = 0
-50t + tv + -30t2 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-50 + v + -30t) = 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 '(-50 + v + -30t)' equal to zero and attempt to solve:

Simplifying
-50 + v + -30t = 0

Reorder the terms:
-50 + -30t + v = 0

Solving
-50 + -30t + v = 0

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

Add '50' to each side of the equation.
-50 + -30t + 50 + v = 0 + 50

Reorder the terms:
-50 + 50 + -30t + v = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -30t + v = 0 + 50
-30t + v = 0 + 50

Combine like terms: 0 + 50 = 50
-30t + v = 50

Add '-1v' to each side of the equation.
-30t + v + -1v = 50 + -1v

Combine like terms: v + -1v = 0
-30t + 0 = 50 + -1v
-30t = 50 + -1v

Divide each side by '-30'.
t = -1.666666667 + 0.03333333333v

Simplifying
t = -1.666666667 + 0.03333333333v
Solution
t = {0, -1.666666667 + 0.03333333333v}

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