144=-16t^2+32t+128

Solution for 144=-16t^2+32t+128 equation:

Simplifying
144 = -16t2 + 32t + 128

Reorder the terms:
144 = 128 + 32t + -16t2

Solving
144 = 128 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 144 + -128 = 16
16 + -32t + 16t2 = 128 + 32t + -16t2 + -128 + -32t + 16t2

Reorder the terms:
16 + -32t + 16t2 = 128 + -128 + 32t + -32t + -16t2 + 16t2

Combine like terms: 128 + -128 = 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 + -1t)(1 + -1t)) = 0

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

Simplifying
1 + -1t = 0

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

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

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

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {1, 1}