-16t^2+384t+4=1284

Solution for -16t^2+384t+4=1284 equation:

Simplifying
-16t2 + 384t + 4 = 1284

Reorder the terms:
4 + 384t + -16t2 = 1284

Solving
4 + 384t + -16t2 = 1284

Solving for variable 't'.

Reorder the terms:
4 + -1284 + 384t + -16t2 = 1284 + -1284

Combine like terms: 4 + -1284 = -1280
-1280 + 384t + -16t2 = 1284 + -1284

Combine like terms: 1284 + -1284 = 0
-1280 + 384t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-80 + 24t + -1t2) = 0

Factor a trinomial.
16((-20 + t)(4 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-20 + t)' equal to zero and attempt to solve:

Simplifying
-20 + t = 0

Solving
-20 + t = 0

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

Add '20' to each side of the equation.
-20 + 20 + t = 0 + 20

Combine like terms: -20 + 20 = 0
0 + t = 0 + 20
t = 0 + 20

Combine like terms: 0 + 20 = 20
t = 20

Simplifying
t = 20
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 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 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {20, 4}