(4t-1)(t+5)=-20

Solution for (4t-1)(t+5)=-20 equation:

Simplifying
(4t + -1)(t + 5) = -20

Reorder the terms:
(-1 + 4t)(t + 5) = -20

Reorder the terms:
(-1 + 4t)(5 + t) = -20

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

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

Solving
-5 + 19t + 4t2 = -20

Solving for variable 't'.

Reorder the terms:
-5 + 20 + 19t + 4t2 = -20 + 20

Combine like terms: -5 + 20 = 15
15 + 19t + 4t2 = -20 + 20

Combine like terms: -20 + 20 = 0
15 + 19t + 4t2 = 0

Factor a trinomial.
(15 + 4t)(1 + t) = 0

Subproblem 1
Set the factor '(15 + 4t)' equal to zero and attempt to solve:

Simplifying
15 + 4t = 0

Solving
15 + 4t = 0

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

Add '-15' to each side of the equation.
15 + -15 + 4t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 4t = 0 + -15
4t = 0 + -15

Combine like terms: 0 + -15 = -15
4t = -15

Divide each side by '4'.
t = -3.75

Simplifying
t = -3.75
Subproblem 2
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
Solution
t = {-3.75, -1}