(4t-1)(t+2)=-5

Solution for (4t-1)(t+2)=-5 equation:

Simplifying
(4t + -1)(t + 2) = -5

Reorder the terms:
(-1 + 4t)(t + 2) = -5

Reorder the terms:
(-1 + 4t)(2 + t) = -5

Multiply (-1 + 4t) * (2 + t)
(-1(2 + t) + 4t * (2 + t)) = -5
((2 * -1 + t * -1) + 4t * (2 + t)) = -5
((-2 + -1t) + 4t * (2 + t)) = -5
(-2 + -1t + (2 * 4t + t * 4t)) = -5
(-2 + -1t + (8t + 4t2)) = -5

Combine like terms: -1t + 8t = 7t
(-2 + 7t + 4t2) = -5

Solving
-2 + 7t + 4t2 = -5

Solving for variable 't'.

Reorder the terms:
-2 + 5 + 7t + 4t2 = -5 + 5

Combine like terms: -2 + 5 = 3
3 + 7t + 4t2 = -5 + 5

Combine like terms: -5 + 5 = 0
3 + 7t + 4t2 = 0

Factor a trinomial.
(1 + t)(3 + 4t) = 0

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

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 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 + 4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4t = 0 + -3
4t = 0 + -3

Combine like terms: 0 + -3 = -3
4t = -3

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
Solution
t = {-1, -0.75}