(4t-1)(t+5)=-27

Solution for (4t-1)(t+5)=-27 equation:

Simplifying
(4t + -1)(t + 5) = -27

Reorder the terms:
(-1 + 4t)(t + 5) = -27

Reorder the terms:
(-1 + 4t)(5 + t) = -27

Multiply (-1 + 4t) * (5 + t)
(-1(5 + t) + 4t * (5 + t)) = -27
((5 * -1 + t * -1) + 4t * (5 + t)) = -27
((-5 + -1t) + 4t * (5 + t)) = -27
(-5 + -1t + (5 * 4t + t * 4t)) = -27
(-5 + -1t + (20t + 4t2)) = -27

Combine like terms: -1t + 20t = 19t
(-5 + 19t + 4t2) = -27

Solving
-5 + 19t + 4t2 = -27

Solving for variable 't'.

Reorder the terms:
-5 + 27 + 19t + 4t2 = -27 + 27

Combine like terms: -5 + 27 = 22
22 + 19t + 4t2 = -27 + 27

Combine like terms: -27 + 27 = 0
22 + 19t + 4t2 = 0

Factor a trinomial.
(11 + 4t)(2 + t) = 0

Subproblem 1
Set the factor '(11 + 4t)' equal to zero and attempt to solve:

Simplifying
11 + 4t = 0

Solving
11 + 4t = 0

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

Add '-11' to each side of the equation.
11 + -11 + 4t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 4t = 0 + -11
4t = 0 + -11

Combine like terms: 0 + -11 = -11
4t = -11

Divide each side by '4'.
t = -2.75

Simplifying
t = -2.75
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {-2.75, -2}