6t(t+2)=5t-2

Solution for 6t(t+2)=5t-2 equation:

Simplifying
6t(t + 2) = 5t + -2

Reorder the terms:
6t(2 + t) = 5t + -2
(2 * 6t + t * 6t) = 5t + -2
(12t + 6t2) = 5t + -2

Reorder the terms:
12t + 6t2 = -2 + 5t

Solving
12t + 6t2 = -2 + 5t

Solving for variable 't'.

Reorder the terms:
2 + 12t + -5t + 6t2 = -2 + 5t + 2 + -5t

Combine like terms: 12t + -5t = 7t
2 + 7t + 6t2 = -2 + 5t + 2 + -5t

Reorder the terms:
2 + 7t + 6t2 = -2 + 2 + 5t + -5t

Combine like terms: -2 + 2 = 0
2 + 7t + 6t2 = 0 + 5t + -5t
2 + 7t + 6t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
2 + 7t + 6t2 = 0

Factor a trinomial.
(2 + 3t)(1 + 2t) = 0

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

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {-0.6666666667, -0.5}