0=16(t^2-5t-6)

Solution for 0=16(t^2-5t-6) equation:

Simplifying
0 = 16(t2 + -5t + -6)

Reorder the terms:
0 = 16(-6 + -5t + t2)
0 = (-6 * 16 + -5t * 16 + t2 * 16)
0 = (-96 + -80t + 16t2)

Solving
0 = -96 + -80t + 16t2

Solving for variable 't'.

Combine like terms: 0 + 96 = 96
96 + 80t + -16t2 = -96 + -80t + 16t2 + 96 + 80t + -16t2

Reorder the terms:
96 + 80t + -16t2 = -96 + 96 + -80t + 80t + 16t2 + -16t2

Combine like terms: -96 + 96 = 0
96 + 80t + -16t2 = 0 + -80t + 80t + 16t2 + -16t2
96 + 80t + -16t2 = -80t + 80t + 16t2 + -16t2

Combine like terms: -80t + 80t = 0
96 + 80t + -16t2 = 0 + 16t2 + -16t2
96 + 80t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
96 + 80t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(6 + 5t + -1t2) = 0

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

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

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
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 = {6, -1}