-14t^2+84t-112=0

Solution for -14t^2+84t-112=0 equation:

Simplifying
-14t2 + 84t + -112 = 0

Reorder the terms:
-112 + 84t + -14t2 = 0

Solving
-112 + 84t + -14t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '14'.
14(-8 + 6t + -1t2) = 0

Factor a trinomial.
14((-4 + t)(2 + -1t)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve:

Simplifying
-4 + t = 0

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

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

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

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {4, 2}