4t^2+5t+1=0

Solution for 4t^2+5t+1=0 equation:

Simplifying
4t2 + 5t + 1 = 0

Reorder the terms:
1 + 5t + 4t2 = 0

Solving
1 + 5t + 4t2 = 0

Solving for variable 't'.

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

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 + 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
Solution
t = {-1, -0.25}