21=-16t^2-32t+5

Solution for 21=-16t^2-32t+5 equation:

Simplifying
21 = -16t2 + -32t + 5

Reorder the terms:
21 = 5 + -32t + -16t2

Solving
21 = 5 + -32t + -16t2

Solving for variable 't'.

Combine like terms: 21 + -5 = 16
16 + 32t + 16t2 = 5 + -32t + -16t2 + -5 + 32t + 16t2

Reorder the terms:
16 + 32t + 16t2 = 5 + -5 + -32t + 32t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
16 + 32t + 16t2 = 0 + -32t + 32t + -16t2 + 16t2
16 + 32t + 16t2 = -32t + 32t + -16t2 + 16t2

Combine like terms: -32t + 32t = 0
16 + 32t + 16t2 = 0 + -16t2 + 16t2
16 + 32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
16 + 32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(1 + 2t + t2) = 0

Factor a trinomial.
16((1 + t)(1 + t)) = 0

Ignore the factor 16.
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 '(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 = {-1, -1}