3t(t-5)+6t^2=

Solution for 3t(t-5)+6t^2= equation:

Simplifying
3t(t + -5) + 6t2 = 0

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

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

Solving
-15t + 9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(-5 + 3t) = 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 '(-5 + 3t)' equal to zero and attempt to solve:

Simplifying
-5 + 3t = 0

Solving
-5 + 3t = 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 + 3t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3t = 0 + 5
3t = 0 + 5

Combine like terms: 0 + 5 = 5
3t = 5

Divide each side by '3'.
t = 1.666666667

Simplifying
t = 1.666666667
Solution
t = {0, 1.666666667}