15t(t+1)=4t-2

Solution for 15t(t+1)=4t-2 equation:

Simplifying
15t(t + 1) = 4t + -2

Reorder the terms:
15t(1 + t) = 4t + -2
(1 * 15t + t * 15t) = 4t + -2
(15t + 15t2) = 4t + -2

Reorder the terms:
15t + 15t2 = -2 + 4t

Solving
15t + 15t2 = -2 + 4t

Solving for variable 't'.

Reorder the terms:
2 + 15t + -4t + 15t2 = -2 + 4t + 2 + -4t

Combine like terms: 15t + -4t = 11t
2 + 11t + 15t2 = -2 + 4t + 2 + -4t

Reorder the terms:
2 + 11t + 15t2 = -2 + 2 + 4t + -4t

Combine like terms: -2 + 2 = 0
2 + 11t + 15t2 = 0 + 4t + -4t
2 + 11t + 15t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
2 + 11t + 15t2 = 0

Factor a trinomial.
(2 + 5t)(1 + 3t) = 0

Subproblem 1
Set the factor '(2 + 5t)' equal to zero and attempt to solve:

Simplifying
2 + 5t = 0

Solving
2 + 5t = 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 + 5t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5t = 0 + -2
5t = 0 + -2

Combine like terms: 0 + -2 = -2
5t = -2

Divide each side by '5'.
t = -0.4

Simplifying
t = -0.4
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 = {-0.4, -0.3333333333}