8t(t+3)=2t-5

Solution for 8t(t+3)=2t-5 equation:

Simplifying
8t(t + 3) = 2t + -5

Reorder the terms:
8t(3 + t) = 2t + -5
(3 * 8t + t * 8t) = 2t + -5
(24t + 8t2) = 2t + -5

Reorder the terms:
24t + 8t2 = -5 + 2t

Solving
24t + 8t2 = -5 + 2t

Solving for variable 't'.

Reorder the terms:
5 + 24t + -2t + 8t2 = -5 + 2t + 5 + -2t

Combine like terms: 24t + -2t = 22t
5 + 22t + 8t2 = -5 + 2t + 5 + -2t

Reorder the terms:
5 + 22t + 8t2 = -5 + 5 + 2t + -2t

Combine like terms: -5 + 5 = 0
5 + 22t + 8t2 = 0 + 2t + -2t
5 + 22t + 8t2 = 2t + -2t

Combine like terms: 2t + -2t = 0
5 + 22t + 8t2 = 0

Factor a trinomial.
(5 + 2t)(1 + 4t) = 0

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

Simplifying
5 + 2t = 0

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

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

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

Divide each side by '2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 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 + 4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4t = 0 + -1
4t = 0 + -1

Combine like terms: 0 + -1 = -1
4t = -1

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {-2.5, -0.25}