8t(t+4)=6t-15

Solution for 8t(t+4)=6t-15 equation:

Simplifying
8t(t + 4) = 6t + -15

Reorder the terms:
8t(4 + t) = 6t + -15
(4 * 8t + t * 8t) = 6t + -15
(32t + 8t2) = 6t + -15

Reorder the terms:
32t + 8t2 = -15 + 6t

Solving
32t + 8t2 = -15 + 6t

Solving for variable 't'.

Reorder the terms:
15 + 32t + -6t + 8t2 = -15 + 6t + 15 + -6t

Combine like terms: 32t + -6t = 26t
15 + 26t + 8t2 = -15 + 6t + 15 + -6t

Reorder the terms:
15 + 26t + 8t2 = -15 + 15 + 6t + -6t

Combine like terms: -15 + 15 = 0
15 + 26t + 8t2 = 0 + 6t + -6t
15 + 26t + 8t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
15 + 26t + 8t2 = 0

Factor a trinomial.
(5 + 2t)(3 + 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 '(3 + 4t)' equal to zero and attempt to solve:

Simplifying
3 + 4t = 0

Solving
3 + 4t = 0

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

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

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

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

Divide each side by '4'.
t = -0.75

Simplifying
t = -0.75
Solution
t = {-2.5, -0.75}