(4t-1)(t+5)=-26

Solution for (4t-1)(t+5)=-26 equation:

Simplifying
(4t + -1)(t + 5) = -26

Reorder the terms:
(-1 + 4t)(t + 5) = -26

Reorder the terms:
(-1 + 4t)(5 + t) = -26

Multiply (-1 + 4t) * (5 + t)
(-1(5 + t) + 4t * (5 + t)) = -26
((5 * -1 + t * -1) + 4t * (5 + t)) = -26
((-5 + -1t) + 4t * (5 + t)) = -26
(-5 + -1t + (5 * 4t + t * 4t)) = -26
(-5 + -1t + (20t + 4t2)) = -26

Combine like terms: -1t + 20t = 19t
(-5 + 19t + 4t2) = -26

Solving
-5 + 19t + 4t2 = -26

Solving for variable 't'.

Reorder the terms:
-5 + 26 + 19t + 4t2 = -26 + 26

Combine like terms: -5 + 26 = 21
21 + 19t + 4t2 = -26 + 26

Combine like terms: -26 + 26 = 0
21 + 19t + 4t2 = 0

Factor a trinomial.
(3 + t)(7 + 4t) = 0

Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

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

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

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

Simplifying
t = -3
Subproblem 2
Set the factor '(7 + 4t)' equal to zero and attempt to solve:

Simplifying
7 + 4t = 0

Solving
7 + 4t = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4t = 0 + -7
4t = 0 + -7

Combine like terms: 0 + -7 = -7
4t = -7

Divide each side by '4'.
t = -1.75

Simplifying
t = -1.75
Solution
t = {-3, -1.75}