40=-2t^2+2t+40

Solution for 40=-2t^2+2t+40 equation:

Simplifying
40 = -2t2 + 2t + 40

Reorder the terms:
40 = 40 + 2t + -2t2

Add '-40' to each side of the equation.
40 + -40 = 40 + 2t + -40 + -2t2

Combine like terms: 40 + -40 = 0
0 = 40 + 2t + -40 + -2t2

Reorder the terms:
0 = 40 + -40 + 2t + -2t2

Combine like terms: 40 + -40 = 0
0 = 0 + 2t + -2t2
0 = 2t + -2t2

Solving
0 = 2t + -2t2

Solving for variable 't'.
Remove the zero:
-2t + 2t2 = 2t + -2t2 + -2t + 2t2

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

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

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

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

Ignore the factor 2.
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 '(-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 = {0, 1}