12t(t+2)=t-10

Solution for 12t(t+2)=t-10 equation:

Simplifying
12t(t + 2) = t + -10

Reorder the terms:
12t(2 + t) = t + -10
(2 * 12t + t * 12t) = t + -10
(24t + 12t2) = t + -10

Reorder the terms:
24t + 12t2 = -10 + t

Solving
24t + 12t2 = -10 + t

Solving for variable 't'.

Reorder the terms:
10 + 24t + -1t + 12t2 = -10 + t + 10 + -1t

Combine like terms: 24t + -1t = 23t
10 + 23t + 12t2 = -10 + t + 10 + -1t

Reorder the terms:
10 + 23t + 12t2 = -10 + 10 + t + -1t

Combine like terms: -10 + 10 = 0
10 + 23t + 12t2 = 0 + t + -1t
10 + 23t + 12t2 = t + -1t

Combine like terms: t + -1t = 0
10 + 23t + 12t2 = 0

Factor a trinomial.
(5 + 4t)(2 + 3t) = 0

Subproblem 1
Set the factor '(5 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve:

Simplifying
2 + 3t = 0

Solving
2 + 3t = 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 + 3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t = 0 + -2
3t = 0 + -2

Combine like terms: 0 + -2 = -2
3t = -2

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {-1.25, -0.6666666667}