-4t^2+24t+13=0

Solution for -4t^2+24t+13=0 equation:

Simplifying
-4t2 + 24t + 13 = 0

Reorder the terms:
13 + 24t + -4t2 = 0

Solving
13 + 24t + -4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(13 + -2t)(1 + 2t) = 0

Subproblem 1
Set the factor '(13 + -2t)' equal to zero and attempt to solve:

Simplifying
13 + -2t = 0

Solving
13 + -2t = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2t = 0 + -13
-2t = 0 + -13

Combine like terms: 0 + -13 = -13
-2t = -13

Divide each side by '-2'.
t = 6.5

Simplifying
t = 6.5
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 = {6.5, -0.5}