6t(t+3)=t-12

Solution for 6t(t+3)=t-12 equation:

Simplifying
6t(t + 3) = t + -12

Reorder the terms:
6t(3 + t) = t + -12
(3 * 6t + t * 6t) = t + -12
(18t + 6t2) = t + -12

Reorder the terms:
18t + 6t2 = -12 + t

Solving
18t + 6t2 = -12 + t

Solving for variable 't'.

Reorder the terms:
12 + 18t + -1t + 6t2 = -12 + t + 12 + -1t

Combine like terms: 18t + -1t = 17t
12 + 17t + 6t2 = -12 + t + 12 + -1t

Reorder the terms:
12 + 17t + 6t2 = -12 + 12 + t + -1t

Combine like terms: -12 + 12 = 0
12 + 17t + 6t2 = 0 + t + -1t
12 + 17t + 6t2 = t + -1t

Combine like terms: t + -1t = 0
12 + 17t + 6t2 = 0

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

Subproblem 1
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

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

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

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

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 2
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
Solution
t = {-1.5, -1.333333333}