(2t-1)(t+5)=-12

Solution for (2t-1)(t+5)=-12 equation:

Simplifying
(2t + -1)(t + 5) = -12

Reorder the terms:
(-1 + 2t)(t + 5) = -12

Reorder the terms:
(-1 + 2t)(5 + t) = -12

Multiply (-1 + 2t) * (5 + t)
(-1(5 + t) + 2t * (5 + t)) = -12
((5 * -1 + t * -1) + 2t * (5 + t)) = -12
((-5 + -1t) + 2t * (5 + t)) = -12
(-5 + -1t + (5 * 2t + t * 2t)) = -12
(-5 + -1t + (10t + 2t2)) = -12

Combine like terms: -1t + 10t = 9t
(-5 + 9t + 2t2) = -12

Solving
-5 + 9t + 2t2 = -12

Solving for variable 't'.

Reorder the terms:
-5 + 12 + 9t + 2t2 = -12 + 12

Combine like terms: -5 + 12 = 7
7 + 9t + 2t2 = -12 + 12

Combine like terms: -12 + 12 = 0
7 + 9t + 2t2 = 0

Factor a trinomial.
(7 + 2t)(1 + t) = 0

Subproblem 1
Set the factor '(7 + 2t)' equal to zero and attempt to solve:

Simplifying
7 + 2t = 0

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

Combine like terms: 7 + -7 = 0
0 + 2t = 0 + -7
2t = 0 + -7

Combine like terms: 0 + -7 = -7
2t = -7

Divide each side by '2'.
t = -3.5

Simplifying
t = -3.5
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 = {-3.5, -1}