20t^2=-t+1

Solution for 20t^2=-t+1 equation:

Simplifying
20t2 = -1t + 1

Reorder the terms:
20t2 = 1 + -1t

Solving
20t2 = 1 + -1t

Solving for variable 't'.

Reorder the terms:
-1 + t + 20t2 = 1 + -1t + -1 + t

Reorder the terms:
-1 + t + 20t2 = 1 + -1 + -1t + t

Combine like terms: 1 + -1 = 0
-1 + t + 20t2 = 0 + -1t + t
-1 + t + 20t2 = -1t + t

Combine like terms: -1t + t = 0
-1 + t + 20t2 = 0

Factor a trinomial.
(-1 + -4t)(1 + -5t) = 0

Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve:

Simplifying
-1 + -4t = 0

Solving
-1 + -4t = 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 + -4t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4t = 0 + 1
-4t = 0 + 1

Combine like terms: 0 + 1 = 1
-4t = 1

Divide each side by '-4'.
t = -0.25

Simplifying
t = -0.25
Subproblem 2
Set the factor '(1 + -5t)' equal to zero and attempt to solve:

Simplifying
1 + -5t = 0

Solving
1 + -5t = 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 + -5t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5t = 0 + -1
-5t = 0 + -1

Combine like terms: 0 + -1 = -1
-5t = -1

Divide each side by '-5'.
t = 0.2

Simplifying
t = 0.2
Solution
t = {-0.25, 0.2}