12t(t+2)=7t-6

Solution for 12t(t+2)=7t-6 equation:

Simplifying
12t(t + 2) = 7t + -6

Reorder the terms:
12t(2 + t) = 7t + -6
(2 * 12t + t * 12t) = 7t + -6
(24t + 12t2) = 7t + -6

Reorder the terms:
24t + 12t2 = -6 + 7t

Solving
24t + 12t2 = -6 + 7t

Solving for variable 't'.

Reorder the terms:
6 + 24t + -7t + 12t2 = -6 + 7t + 6 + -7t

Combine like terms: 24t + -7t = 17t
6 + 17t + 12t2 = -6 + 7t + 6 + -7t

Reorder the terms:
6 + 17t + 12t2 = -6 + 6 + 7t + -7t

Combine like terms: -6 + 6 = 0
6 + 17t + 12t2 = 0 + 7t + -7t
6 + 17t + 12t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
6 + 17t + 12t2 = 0

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

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

Simplifying
3 + 4t = 0

Solving
3 + 4t = 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 + 4t = 0 + -3

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

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

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
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 = {-0.75, -0.6666666667}