-16t^2+128t-112=0

Solution for -16t^2+128t-112=0 equation:

Simplifying
-16t2 + 128t + -112 = 0

Reorder the terms:
-112 + 128t + -16t2 = 0

Solving
-112 + 128t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-7 + 8t + -1t2) = 0

Factor a trinomial.
16((-7 + t)(1 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve:

Simplifying
-7 + t = 0

Solving
-7 + t = 0

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

Add '7' to each side of the equation.
-7 + 7 + t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + t = 0 + 7
t = 0 + 7

Combine like terms: 0 + 7 = 7
t = 7

Simplifying
t = 7
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 = {7, 1}