0=80+30t-5t^2

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Solution for 0=80+30t-5t^2 equation: 


Simplifying
0 = 80 + 30t + -5t2

Solving
0 = 80 + 30t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -80 = -80
-80 + -30t + 5t2 = 80 + 30t + -5t2 + -80 + -30t + 5t2

Reorder the terms:
-80 + -30t + 5t2 = 80 + -80 + 30t + -30t + -5t2 + 5t2

Combine like terms: 80 + -80 = 0
-80 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2
-80 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2

Combine like terms: 30t + -30t = 0
-80 + -30t + 5t2 = 0 + -5t2 + 5t2
-80 + -30t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-80 + -30t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -6t + t2) = 0

Factor a trinomial.
5((-2 + -1t)(8 + -1t)) = 0

Ignore the factor 5.

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2

Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {-2, 8}

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