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

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

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

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

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

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

Combine like terms: 1t + -14t = -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((-1 + -2t)(7 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
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
Subproblem 2
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
Solution
t = {-0.5, 7}