40=40-10t-5t^2

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


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

Add '-40' to each side of the equation.
40 + -40 = 40 + -10t + -40 + -5t2

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

Reorder the terms:
0 = 40 + -40 + -10t + -5t2

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

Solving
0 = -10t + -5t2

Solving for variable 't'.
Remove the zero:
10t + 5t2 = -10t + -5t2 + 10t + 5t2

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

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

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

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

Ignore the factor 5.

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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {0, -2}

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