3t(t-5)+6t=

Solution for 3t(t-5)+6t= equation:

Simplifying
3t(t + -5) + 6t = 0

Reorder the terms:
3t(-5 + t) + 6t = 0
(-5 * 3t + t * 3t) + 6t = 0
(-15t + 3t2) + 6t = 0

Reorder the terms:
-15t + 6t + 3t2 = 0

Combine like terms: -15t + 6t = -9t
-9t + 3t2 = 0

Solving
-9t + 3t2 = 0

Solving for variable 't'.

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

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

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
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
Solution
t = {0, 3}