15t(t+2)=t-12

Solution for 15t(t+2)=t-12 equation:

Simplifying
15t(t + 2) = t + -12

Reorder the terms:
15t(2 + t) = t + -12
(2 * 15t + t * 15t) = t + -12
(30t + 15t2) = t + -12

Reorder the terms:
30t + 15t2 = -12 + t

Solving
30t + 15t2 = -12 + t

Solving for variable 't'.

Reorder the terms:
12 + 30t + -1t + 15t2 = -12 + t + 12 + -1t

Combine like terms: 30t + -1t = 29t
12 + 29t + 15t2 = -12 + t + 12 + -1t

Reorder the terms:
12 + 29t + 15t2 = -12 + 12 + t + -1t

Combine like terms: -12 + 12 = 0
12 + 29t + 15t2 = 0 + t + -1t
12 + 29t + 15t2 = t + -1t

Combine like terms: t + -1t = 0
12 + 29t + 15t2 = 0

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

Subproblem 1
Set the factor '(4 + 3t)' equal to zero and attempt to solve:

Simplifying
4 + 3t = 0

Solving
4 + 3t = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3t = 0 + -4
3t = 0 + -4

Combine like terms: 0 + -4 = -4
3t = -4

Divide each side by '3'.
t = -1.333333333

Simplifying
t = -1.333333333
Subproblem 2
Set the factor '(3 + 5t)' equal to zero and attempt to solve:

Simplifying
3 + 5t = 0

Solving
3 + 5t = 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 + 5t = 0 + -3

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

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

Divide each side by '5'.
t = -0.6

Simplifying
t = -0.6
Solution
t = {-1.333333333, -0.6}