4t^2+24t=-32

Solution for 4t^2+24t=-32 equation:

Simplifying
4t2 + 24t = -32

Reorder the terms:
24t + 4t2 = -32

Solving
24t + 4t2 = -32

Solving for variable 't'.

Reorder the terms:
32 + 24t + 4t2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + 24t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 6t + t2) = 0

Factor a trinomial.
4((4 + t)(2 + t)) = 0

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

Simplifying
4 + t = 0

Solving
4 + t = 0

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

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

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

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

Simplifying
t = -4
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

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

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

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

Simplifying
t = -2
Solution
t = {-4, -2}