2t(3t+9)=-3(t+5)

Solution for 2t(3t+9)=-3(t+5) equation:

Simplifying
2t(3t + 9) = -3(t + 5)

Reorder the terms:
2t(9 + 3t) = -3(t + 5)
(9 * 2t + 3t * 2t) = -3(t + 5)
(18t + 6t2) = -3(t + 5)

Reorder the terms:
18t + 6t2 = -3(5 + t)
18t + 6t2 = (5 * -3 + t * -3)
18t + 6t2 = (-15 + -3t)

Solving
18t + 6t2 = -15 + -3t

Solving for variable 't'.

Reorder the terms:
15 + 18t + 3t + 6t2 = -15 + -3t + 15 + 3t

Combine like terms: 18t + 3t = 21t
15 + 21t + 6t2 = -15 + -3t + 15 + 3t

Reorder the terms:
15 + 21t + 6t2 = -15 + 15 + -3t + 3t

Combine like terms: -15 + 15 = 0
15 + 21t + 6t2 = 0 + -3t + 3t
15 + 21t + 6t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
15 + 21t + 6t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 7t + 2t2) = 0

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

Ignore the factor 3.
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 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

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

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

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

Simplifying
t = -1
Solution
t = {-2.5, -1}