6t(2t+1)=5-5t

Solution for 6t(2t+1)=5-5t equation:

Simplifying
6t(2t + 1) = 5 + -5t

Reorder the terms:
6t(1 + 2t) = 5 + -5t
(1 * 6t + 2t * 6t) = 5 + -5t
(6t + 12t2) = 5 + -5t

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

Solving for variable 't'.

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

Combine like terms: 6t + 5t = 11t
-5 + 11t + 12t2 = 5 + -5t + -5 + 5t

Reorder the terms:
-5 + 11t + 12t2 = 5 + -5 + -5t + 5t

Combine like terms: 5 + -5 = 0
-5 + 11t + 12t2 = 0 + -5t + 5t
-5 + 11t + 12t2 = -5t + 5t

Combine like terms: -5t + 5t = 0
-5 + 11t + 12t2 = 0

Factor a trinomial.
(-5 + -4t)(1 + -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 '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 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 + -3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3t = 0 + -1
-3t = 0 + -1

Combine like terms: 0 + -1 = -1
-3t = -1

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {-1.25, 0.3333333333}