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

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

Simplifying
2(-8t2 + 7t + 1) = 0

Reorder the terms:
2(1 + 7t + -8t2) = 0
(1 * 2 + 7t * 2 + -8t2 * 2) = 0
(2 + 14t + -16t2) = 0

Solving
2 + 14t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 7t + -8t2) = 0

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Subproblem 2
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
Solution
t = {1, -0.125}