12t(t+2)=t-5

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

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

Reorder the terms:
12t(2 + t) = t + -5
(2 * 12t + t * 12t) = t + -5
(24t + 12t2) = t + -5

Reorder the terms:
24t + 12t2 = -5 + t

Solving
24t + 12t2 = -5 + t

Solving for variable 't'.

Reorder the terms:
5 + 24t + -1t + 12t2 = -5 + t + 5 + -1t

Combine like terms: 24t + -1t = 23t
5 + 23t + 12t2 = -5 + t + 5 + -1t

Reorder the terms:
5 + 23t + 12t2 = -5 + 5 + t + -1t

Combine like terms: -5 + 5 = 0
5 + 23t + 12t2 = 0 + t + -1t
5 + 23t + 12t2 = t + -1t

Combine like terms: t + -1t = 0
5 + 23t + 12t2 = 0

Factor a trinomial.
(5 + 3t)(1 + 4t) = 0

Subproblem 1
Set the factor '(5 + 3t)' equal to zero and attempt to solve:

Simplifying
5 + 3t = 0

Solving
5 + 3t = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3t = 0 + -5
3t = 0 + -5

Combine like terms: 0 + -5 = -5
3t = -5

Divide each side by '3'.
t = -1.666666667

Simplifying
t = -1.666666667
Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 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 + 4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4t = 0 + -1
4t = 0 + -1

Combine like terms: 0 + -1 = -1
4t = -1

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {-1.666666667, -0.25}