-16t^2+112t+128=224

Solution for -16t^2+112t+128=224 equation:

Simplifying
-16t2 + 112t + 128 = 224

Reorder the terms:
128 + 112t + -16t2 = 224

Solving
128 + 112t + -16t2 = 224

Solving for variable 't'.

Reorder the terms:
128 + -224 + 112t + -16t2 = 224 + -224

Combine like terms: 128 + -224 = -96
-96 + 112t + -16t2 = 224 + -224

Combine like terms: 224 + -224 = 0
-96 + 112t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + 7t + -1t2) = 0

Factor a trinomial.
16((-6 + t)(1 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 0

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

Add '6' to each side of the equation.
-6 + 6 + t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + t = 0 + 6
t = 0 + 6

Combine like terms: 0 + 6 = 6
t = 6

Simplifying
t = 6
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 = {6, 1}