3t(t+1)=2(5t-1)

Solution for 3t(t+1)=2(5t-1) equation:

Simplifying
3t(t + 1) = 2(5t + -1)

Reorder the terms:
3t(1 + t) = 2(5t + -1)
(1 * 3t + t * 3t) = 2(5t + -1)
(3t + 3t2) = 2(5t + -1)

Reorder the terms:
3t + 3t2 = 2(-1 + 5t)
3t + 3t2 = (-1 * 2 + 5t * 2)
3t + 3t2 = (-2 + 10t)

Solving
3t + 3t2 = -2 + 10t

Solving for variable 't'.

Reorder the terms:
2 + 3t + -10t + 3t2 = -2 + 10t + 2 + -10t

Combine like terms: 3t + -10t = -7t
2 + -7t + 3t2 = -2 + 10t + 2 + -10t

Reorder the terms:
2 + -7t + 3t2 = -2 + 2 + 10t + -10t

Combine like terms: -2 + 2 = 0
2 + -7t + 3t2 = 0 + 10t + -10t
2 + -7t + 3t2 = 10t + -10t

Combine like terms: 10t + -10t = 0
2 + -7t + 3t2 = 0

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

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

Simplifying
2 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.3333333333, 2}