4t^2+20t+9=0

Solution for 4t^2+20t+9=0 equation:

Simplifying
4t2 + 20t + 9 = 0

Reorder the terms:
9 + 20t + 4t2 = 0

Solving
9 + 20t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(9 + 2t)(1 + 2t) = 0

Subproblem 1
Set the factor '(9 + 2t)' equal to zero and attempt to solve:

Simplifying
9 + 2t = 0

Solving
9 + 2t = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2t = 0 + -9
2t = 0 + -9

Combine like terms: 0 + -9 = -9
2t = -9

Divide each side by '2'.
t = -4.5

Simplifying
t = -4.5
Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 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 + -1 + 2t = 0 + -1

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

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

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

Simplifying
t = -0.5
Solution
t = {-4.5, -0.5}