6t^2-30t+24=0

Solution for 6t^2-30t+24=0 equation:

Simplifying
6t2 + -30t + 24 = 0

Reorder the terms:
24 + -30t + 6t2 = 0

Solving
24 + -30t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -5t + t2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {1, 4}