0=-2(8t+1)(t-3)

Solution for 0=-2(8t+1)(t-3) equation:

Simplifying
0 = -2(8t + 1)(t + -3)

Reorder the terms:
0 = -2(1 + 8t)(t + -3)

Reorder the terms:
0 = -2(1 + 8t)(-3 + t)

Multiply (1 + 8t) * (-3 + t)
0 = -2(1(-3 + t) + 8t * (-3 + t))
0 = -2((-3 * 1 + t * 1) + 8t * (-3 + t))
0 = -2((-3 + 1t) + 8t * (-3 + t))
0 = -2(-3 + 1t + (-3 * 8t + t * 8t))
0 = -2(-3 + 1t + (-24t + 8t2))

Combine like terms: 1t + -24t = -23t
0 = -2(-3 + -23t + 8t2)
0 = (-3 * -2 + -23t * -2 + 8t2 * -2)
0 = (6 + 46t + -16t2)

Solving
0 = 6 + 46t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -46t + 16t2 = 6 + 46t + -16t2 + -6 + -46t + 16t2

Reorder the terms:
-6 + -46t + 16t2 = 6 + -6 + 46t + -46t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + -46t + 16t2 = 0 + 46t + -46t + -16t2 + 16t2
-6 + -46t + 16t2 = 46t + -46t + -16t2 + 16t2

Combine like terms: 46t + -46t = 0
-6 + -46t + 16t2 = 0 + -16t2 + 16t2
-6 + -46t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -46t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -23t + 8t2) = 0

Factor a trinomial.
2((-1 + -8t)(3 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -8t)' equal to zero and attempt to solve:

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 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 + -8t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8t = 0 + 1
-8t = 0 + 1

Combine like terms: 0 + 1 = 1
-8t = 1

Divide each side by '-8'.
t = -0.125

Simplifying
t = -0.125
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.125, 3}