0=(t-2)(16t+1)

Solution for 0=(t-2)(16t+1) equation:

Simplifying
0 = (t + -2)(16t + 1)

Reorder the terms:
0 = (-2 + t)(16t + 1)

Reorder the terms:
0 = (-2 + t)(1 + 16t)

Multiply (-2 + t) * (1 + 16t)
0 = (-2(1 + 16t) + t(1 + 16t))
0 = ((1 * -2 + 16t * -2) + t(1 + 16t))
0 = ((-2 + -32t) + t(1 + 16t))
0 = (-2 + -32t + (1 * t + 16t * t))
0 = (-2 + -32t + (1t + 16t2))

Combine like terms: -32t + 1t = -31t
0 = (-2 + -31t + 16t2)

Solving
0 = -2 + -31t + 16t2

Solving for variable 't'.

Combine like terms: 0 + 2 = 2
2 + 31t + -16t2 = -2 + -31t + 16t2 + 2 + 31t + -16t2

Reorder the terms:
2 + 31t + -16t2 = -2 + 2 + -31t + 31t + 16t2 + -16t2

Combine like terms: -2 + 2 = 0
2 + 31t + -16t2 = 0 + -31t + 31t + 16t2 + -16t2
2 + 31t + -16t2 = -31t + 31t + 16t2 + -16t2

Combine like terms: -31t + 31t = 0
2 + 31t + -16t2 = 0 + 16t2 + -16t2
2 + 31t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
2 + 31t + -16t2 = 0

Factor a trinomial.
(2 + -1t)(1 + 16t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 16t)' equal to zero and attempt to solve:

Simplifying
1 + 16t = 0

Solving
1 + 16t = 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 + 16t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 16t = 0 + -1
16t = 0 + -1

Combine like terms: 0 + -1 = -1
16t = -1

Divide each side by '16'.
t = -0.0625

Simplifying
t = -0.0625
Solution
t = {2, -0.0625}