-3t(t+5)+(4t+2)=8

Solution for -3t(t+5)+(4t+2)=8 equation:

Simplifying
-3t(t + 5) + (4t + 2) = 8

Reorder the terms:
-3t(5 + t) + (4t + 2) = 8
(5 * -3t + t * -3t) + (4t + 2) = 8
(-15t + -3t2) + (4t + 2) = 8

Reorder the terms:
-15t + -3t2 + (2 + 4t) = 8

Remove parenthesis around (2 + 4t)
-15t + -3t2 + 2 + 4t = 8

Reorder the terms:
2 + -15t + 4t + -3t2 = 8

Combine like terms: -15t + 4t = -11t
2 + -11t + -3t2 = 8

Solving
2 + -11t + -3t2 = 8

Solving for variable 't'.

Reorder the terms:
2 + -8 + -11t + -3t2 = 8 + -8

Combine like terms: 2 + -8 = -6
-6 + -11t + -3t2 = 8 + -8

Combine like terms: 8 + -8 = 0
-6 + -11t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 11t + 3t2) = 0

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

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

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

Simplifying
t = -3
Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve:

Simplifying
2 + 3t = 0

Solving
2 + 3t = 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 + 3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3t = 0 + -2
3t = 0 + -2

Combine like terms: 0 + -2 = -2
3t = -2

Divide each side by '3'.
t = -0.6666666667

Simplifying
t = -0.6666666667
Solution
t = {-3, -0.6666666667}