0=5+10t+5t^2

Solution for 0=5+10t+5t^2 equation:

Simplifying
0 = 5 + 10t + 5t2

Solving
0 = 5 + 10t + 5t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-5'.
-5(1 + 2t + t2) = 0

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

Ignore the factor -5.
Subproblem 1
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

Simplifying
t = -1
Solution
t = {-1, -1}