0=100+40t-5t^2

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Solution for 0=100+40t-5t^2 equation: 


Simplifying
0 = 100 + 40t + -5t2

Solving
0 = 100 + 40t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -100 = -100
-100 + -40t + 5t2 = 100 + 40t + -5t2 + -100 + -40t + 5t2

Reorder the terms:
-100 + -40t + 5t2 = 100 + -100 + 40t + -40t + -5t2 + 5t2

Combine like terms: 100 + -100 = 0
-100 + -40t + 5t2 = 0 + 40t + -40t + -5t2 + 5t2
-100 + -40t + 5t2 = 40t + -40t + -5t2 + 5t2

Combine like terms: 40t + -40t = 0
-100 + -40t + 5t2 = 0 + -5t2 + 5t2
-100 + -40t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-100 + -40t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -8t + t2) = 0

Factor a trinomial.
5((-2 + -1t)(10 + -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 '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Solution
t = {-2, 10}

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