-4t^2-7t-3=0

Solution for -4t^2-7t-3=0 equation:

Simplifying
-4t2 + -7t + -3 = 0

Reorder the terms:
-3 + -7t + -4t2 = 0

Solving
-3 + -7t + -4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7t + 4t2) = 0

Factor a trinomial.
-1((1 + t)(3 + 4t)) = 0

Ignore the factor -1.
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 '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4t = 0 + -3
4t = 0 + -3

Combine like terms: 0 + -3 = -3
4t = -3

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
Solution
t = {-1, -0.75}