-8(t-7)(2t+1)=0

Solution for -8(t-7)(2t+1)=0 equation:

Simplifying
-8(t + -7)(2t + 1) = 0

Reorder the terms:
-8(-7 + t)(2t + 1) = 0

Reorder the terms:
-8(-7 + t)(1 + 2t) = 0

Multiply (-7 + t) * (1 + 2t)
-8(-7(1 + 2t) + t(1 + 2t)) = 0
-8((1 * -7 + 2t * -7) + t(1 + 2t)) = 0
-8((-7 + -14t) + t(1 + 2t)) = 0
-8(-7 + -14t + (1 * t + 2t * t)) = 0
-8(-7 + -14t + (1t + 2t2)) = 0

Combine like terms: -14t + 1t = -13t
-8(-7 + -13t + 2t2) = 0
(-7 * -8 + -13t * -8 + 2t2 * -8) = 0
(56 + 104t + -16t2) = 0

Solving
56 + 104t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(7 + 13t + -2t2) = 0

Factor a trinomial.
8((7 + -1t)(1 + 2t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 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 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

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

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

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {7, -0.5}