(2t+1)(4t-1)=14

Solution for (2t+1)(4t-1)=14 equation:

Simplifying
(2t + 1)(4t + -1) = 14

Reorder the terms:
(1 + 2t)(4t + -1) = 14

Reorder the terms:
(1 + 2t)(-1 + 4t) = 14

Multiply (1 + 2t) * (-1 + 4t)
(1(-1 + 4t) + 2t * (-1 + 4t)) = 14
((-1 * 1 + 4t * 1) + 2t * (-1 + 4t)) = 14
((-1 + 4t) + 2t * (-1 + 4t)) = 14
(-1 + 4t + (-1 * 2t + 4t * 2t)) = 14
(-1 + 4t + (-2t + 8t2)) = 14

Combine like terms: 4t + -2t = 2t
(-1 + 2t + 8t2) = 14

Solving
-1 + 2t + 8t2 = 14

Solving for variable 't'.

Reorder the terms:
-1 + -14 + 2t + 8t2 = 14 + -14

Combine like terms: -1 + -14 = -15
-15 + 2t + 8t2 = 14 + -14

Combine like terms: 14 + -14 = 0
-15 + 2t + 8t2 = 0

Factor a trinomial.
(-3 + -2t)(5 + -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 '(5 + -4t)' equal to zero and attempt to solve:

Simplifying
5 + -4t = 0

Solving
5 + -4t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4t = 0 + -5
-4t = 0 + -5

Combine like terms: 0 + -5 = -5
-4t = -5

Divide each side by '-4'.
t = 1.25

Simplifying
t = 1.25
Solution
t = {-1.5, 1.25}