8t^2-2t-21=0

Solution for 8t^2-2t-21=0 equation:

Simplifying
8t2 + -2t + -21 = 0

Reorder the terms:
-21 + -2t + 8t2 = 0

Solving
-21 + -2t + 8t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -2t)(7 + -4t) = 0

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

Simplifying
-3 + -2t = 0

Solving
-3 + -2t = 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 + -2t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2t = 0 + 3
-2t = 0 + 3

Combine like terms: 0 + 3 = 3
-2t = 3

Divide each side by '-2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
Set the factor '(7 + -4t)' equal to zero and attempt to solve:

Simplifying
7 + -4t = 0

Solving
7 + -4t = 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 + -4t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4t = 0 + -7
-4t = 0 + -7

Combine like terms: 0 + -7 = -7
-4t = -7

Divide each side by '-4'.
t = 1.75

Simplifying
t = 1.75
Solution
t = {-1.5, 1.75}