15t(t+2)=7t-4

Solution for 15t(t+2)=7t-4 equation:

Simplifying
15t(t + 2) = 7t + -4

Reorder the terms:
15t(2 + t) = 7t + -4
(2 * 15t + t * 15t) = 7t + -4
(30t + 15t2) = 7t + -4

Reorder the terms:
30t + 15t2 = -4 + 7t

Solving
30t + 15t2 = -4 + 7t

Solving for variable 't'.

Reorder the terms:
4 + 30t + -7t + 15t2 = -4 + 7t + 4 + -7t

Combine like terms: 30t + -7t = 23t
4 + 23t + 15t2 = -4 + 7t + 4 + -7t

Reorder the terms:
4 + 23t + 15t2 = -4 + 4 + 7t + -7t

Combine like terms: -4 + 4 = 0
4 + 23t + 15t2 = 0 + 7t + -7t
4 + 23t + 15t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
4 + 23t + 15t2 = 0

Factor a trinomial.
(4 + 3t)(1 + 5t) = 0

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

Simplifying
4 + 3t = 0

Solving
4 + 3t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3t = 0 + -4

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

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

Divide each side by '3'.
t = -1.333333333

Simplifying
t = -1.333333333
Subproblem 2
Set the factor '(1 + 5t)' equal to zero and attempt to solve:

Simplifying
1 + 5t = 0

Solving
1 + 5t = 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 + 5t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5t = 0 + -1
5t = 0 + -1

Combine like terms: 0 + -1 = -1
5t = -1

Divide each side by '5'.
t = -0.2

Simplifying
t = -0.2
Solution
t = {-1.333333333, -0.2}