0=6t^2-30t+36

Solution for 0=6t^2-30t+36 equation:

Simplifying
0 = 6t2 + -30t + 36

Reorder the terms:
0 = 36 + -30t + 6t2

Solving
0 = 36 + -30t + 6t2

Solving for variable 't'.

Combine like terms: 0 + -36 = -36
-36 + 30t + -6t2 = 36 + -30t + 6t2 + -36 + 30t + -6t2

Reorder the terms:
-36 + 30t + -6t2 = 36 + -36 + -30t + 30t + 6t2 + -6t2

Combine like terms: 36 + -36 = 0
-36 + 30t + -6t2 = 0 + -30t + 30t + 6t2 + -6t2
-36 + 30t + -6t2 = -30t + 30t + 6t2 + -6t2

Combine like terms: -30t + 30t = 0
-36 + 30t + -6t2 = 0 + 6t2 + -6t2
-36 + 30t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
-36 + 30t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + 5t + -1t2) = 0

Factor a trinomial.
6((-3 + t)(2 + -1t)) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

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