4t^2+24t=-20

Solution for 4t^2+24t=-20 equation:

Simplifying
4t2 + 24t = -20

Reorder the terms:
24t + 4t2 = -20

Solving
24t + 4t2 = -20

Solving for variable 't'.

Reorder the terms:
20 + 24t + 4t2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + 24t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 6t + t2) = 0

Factor a trinomial.
4((5 + t)(1 + t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 0

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

Add '-5' to each side of the equation.
5 + -5 + t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + t = 0 + -5
t = 0 + -5

Combine like terms: 0 + -5 = -5
t = -5

Simplifying
t = -5
Subproblem 2
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
Solution
t = {-5, -1}