-4t^2-60t-29=0

Solution for -4t^2-60t-29=0 equation:

Simplifying
-4t2 + -60t + -29 = 0

Reorder the terms:
-29 + -60t + -4t2 = 0

Solving
-29 + -60t + -4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(29 + 60t + 4t2) = 0

Factor a trinomial.
-1((29 + 2t)(1 + 2t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(29 + 2t)' equal to zero and attempt to solve:

Simplifying
29 + 2t = 0

Solving
29 + 2t = 0

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

Add '-29' to each side of the equation.
29 + -29 + 2t = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 2t = 0 + -29
2t = 0 + -29

Combine like terms: 0 + -29 = -29
2t = -29

Divide each side by '2'.
t = -14.5

Simplifying
t = -14.5
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 = {-14.5, -0.5}