0=40-10t-5t^2

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Solution for 0=40-10t-5t^2 equation: 


Simplifying
0 = 40 + -10t + -5t2

Solving
0 = 40 + -10t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -40 = -40
-40 + 10t + 5t2 = 40 + -10t + -5t2 + -40 + 10t + 5t2

Reorder the terms:
-40 + 10t + 5t2 = 40 + -40 + -10t + 10t + -5t2 + 5t2

Combine like terms: 40 + -40 = 0
-40 + 10t + 5t2 = 0 + -10t + 10t + -5t2 + 5t2
-40 + 10t + 5t2 = -10t + 10t + -5t2 + 5t2

Combine like terms: -10t + 10t = 0
-40 + 10t + 5t2 = 0 + -5t2 + 5t2
-40 + 10t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-40 + 10t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + 2t + t2) = 0

Factor a trinomial.
5((-4 + -1t)(2 + -1t)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4

Subproblem 2
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
Solution
t = {-4, 2}

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