1000=80t+2t^2

Solution for 1000=80t+2t^2 equation:

Simplifying
1000 = 80t + 2t2

Solving
1000 = 80t + 2t2

Solving for variable 't'.

Reorder the terms:
1000 + -80t + -2t2 = 80t + -80t + 2t2 + -2t2

Combine like terms: 80t + -80t = 0
1000 + -80t + -2t2 = 0 + 2t2 + -2t2
1000 + -80t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
1000 + -80t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(500 + -40t + -1t2) = 0

Factor a trinomial.
2((10 + -1t)(50 + t)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(50 + t)' equal to zero and attempt to solve:

Simplifying
50 + t = 0

Solving
50 + t = 0

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

Add '-50' to each side of the equation.
50 + -50 + t = 0 + -50

Combine like terms: 50 + -50 = 0
0 + t = 0 + -50
t = 0 + -50

Combine like terms: 0 + -50 = -50
t = -50

Simplifying
t = -50
Solution
t = {10, -50}