(2t-3)(7t+1)=0

Solution for (2t-3)(7t+1)=0 equation:

Simplifying
(2t + -3)(7t + 1) = 0

Reorder the terms:
(-3 + 2t)(7t + 1) = 0

Reorder the terms:
(-3 + 2t)(1 + 7t) = 0

Multiply (-3 + 2t) * (1 + 7t)
(-3(1 + 7t) + 2t * (1 + 7t)) = 0
((1 * -3 + 7t * -3) + 2t * (1 + 7t)) = 0
((-3 + -21t) + 2t * (1 + 7t)) = 0
(-3 + -21t + (1 * 2t + 7t * 2t)) = 0
(-3 + -21t + (2t + 14t2)) = 0

Combine like terms: -21t + 2t = -19t
(-3 + -19t + 14t2) = 0

Solving
-3 + -19t + 14t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -7t)(3 + -2t) = 0

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

Simplifying
-1 + -7t = 0

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

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

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

Divide each side by '-7'.
t = -0.1428571429

Simplifying
t = -0.1428571429
Subproblem 2
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
Solution
t = {-0.1428571429, 1.5}