=3t^2-30t+72

Solution for =3t^2-30t+72 equation:

Simplifying
0 = 3t2 + -30t + 72

Reorder the terms:
0 = 72 + -30t + 3t2

Solving
0 = 72 + -30t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -72 = -72
-72 + 30t + -3t2 = 72 + -30t + 3t2 + -72 + 30t + -3t2

Reorder the terms:
-72 + 30t + -3t2 = 72 + -72 + -30t + 30t + 3t2 + -3t2

Combine like terms: 72 + -72 = 0
-72 + 30t + -3t2 = 0 + -30t + 30t + 3t2 + -3t2
-72 + 30t + -3t2 = -30t + 30t + 3t2 + -3t2

Combine like terms: -30t + 30t = 0
-72 + 30t + -3t2 = 0 + 3t2 + -3t2
-72 + 30t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-72 + 30t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 10t + -1t2) = 0

Factor a trinomial.
3((-6 + t)(4 + -1t)) = 0

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

Simplifying
-6 + t = 0

Solving
-6 + t = 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 + t = 0 + 6

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

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

Simplifying
t = 6
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {6, 4}