(4t+1)(t-2)=0

Solution for (4t+1)(t-2)=0 equation:

Simplifying
(4t + 1)(t + -2) = 0

Reorder the terms:
(1 + 4t)(t + -2) = 0

Reorder the terms:
(1 + 4t)(-2 + t) = 0

Multiply (1 + 4t) * (-2 + t)
(1(-2 + t) + 4t * (-2 + t)) = 0
((-2 * 1 + t * 1) + 4t * (-2 + t)) = 0
((-2 + 1t) + 4t * (-2 + t)) = 0
(-2 + 1t + (-2 * 4t + t * 4t)) = 0
(-2 + 1t + (-8t + 4t2)) = 0

Combine like terms: 1t + -8t = -7t
(-2 + -7t + 4t2) = 0

Solving
-2 + -7t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -4t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-1 + -4t)' equal to zero and attempt to solve:

Simplifying
-1 + -4t = 0

Solving
-1 + -4t = 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 + -4t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4t = 0 + 1
-4t = 0 + 1

Combine like terms: 0 + 1 = 1
-4t = 1

Divide each side by '-4'.
t = -0.25

Simplifying
t = -0.25
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-0.25, 2}