F(t)=t-2t^2

Solution for F(t)=t-2t^2 equation:

Simplifying
F(t) = t + -2t2

Multiply F * t
tF = t + -2t2

Solving
tF = t + -2t2

Solving for variable 't'.

Reorder the terms:
-1t + tF + 2t2 = t + -2t2 + -1t + 2t2

Reorder the terms:
-1t + tF + 2t2 = t + -1t + -2t2 + 2t2

Combine like terms: t + -1t = 0
-1t + tF + 2t2 = 0 + -2t2 + 2t2
-1t + tF + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-1t + tF + 2t2 = 0

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

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

Simplifying
-1 + F + 2t = 0

Solving
-1 + F + 2t = 0

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

Add '1' to each side of the equation.
-1 + F + 1 + 2t = 0 + 1

Reorder the terms:
-1 + 1 + F + 2t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + F + 2t = 0 + 1
F + 2t = 0 + 1

Combine like terms: 0 + 1 = 1
F + 2t = 1

Add '-1F' to each side of the equation.
F + -1F + 2t = 1 + -1F

Combine like terms: F + -1F = 0
0 + 2t = 1 + -1F
2t = 1 + -1F

Divide each side by '2'.
t = 0.5 + -0.5F

Simplifying
t = 0.5 + -0.5F
Solution
t = {0, 0.5 + -0.5F}