-16t^2+64t+128=48

Solution for -16t^2+64t+128=48 equation:

Simplifying
-16t2 + 64t + 128 = 48

Reorder the terms:
128 + 64t + -16t2 = 48

Solving
128 + 64t + -16t2 = 48

Solving for variable 't'.

Reorder the terms:
128 + -48 + 64t + -16t2 = 48 + -48

Combine like terms: 128 + -48 = 80
80 + 64t + -16t2 = 48 + -48

Combine like terms: 48 + -48 = 0
80 + 64t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(5 + 4t + -1t2) = 0

Factor a trinomial.
16((5 + -1t)(1 + t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
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}