0=-5t^2+25t+30

Solution for 0=-5t^2+25t+30 equation:

Simplifying
0 = -5t2 + 25t + 30

Reorder the terms:
0 = 30 + 25t + -5t2

Solving
0 = 30 + 25t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -30 = -30
-30 + -25t + 5t2 = 30 + 25t + -5t2 + -30 + -25t + 5t2

Reorder the terms:
-30 + -25t + 5t2 = 30 + -30 + 25t + -25t + -5t2 + 5t2

Combine like terms: 30 + -30 = 0
-30 + -25t + 5t2 = 0 + 25t + -25t + -5t2 + 5t2
-30 + -25t + 5t2 = 25t + -25t + -5t2 + 5t2

Combine like terms: 25t + -25t = 0
-30 + -25t + 5t2 = 0 + -5t2 + 5t2
-30 + -25t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-30 + -25t + 5t2 = 0

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

Factor a trinomial.
5((-1 + -1t)(6 + -1t)) = 0

Ignore the factor 5.
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 '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-1, 6}