3t(t+5)=18

Solution for 3t(t+5)=18 equation:

Simplifying
3t(t + 5) = 18

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

Solving
15t + 3t2 = 18

Solving for variable 't'.

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

Combine like terms: 18 + -18 = 0
-18 + 15t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 5t + t2) = 0

Factor a trinomial.
3((-6 + -1t)(1 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Solution
t = {-6, 1}