-13t^2+78t=65

Solution for -13t^2+78t=65 equation:

Simplifying
-13t2 + 78t = 65

Reorder the terms:
78t + -13t2 = 65

Solving
78t + -13t2 = 65

Solving for variable 't'.

Reorder the terms:
-65 + 78t + -13t2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + 78t + -13t2 = 0

Factor out the Greatest Common Factor (GCF), '13'.
13(-5 + 6t + -1t2) = 0

Factor a trinomial.
13((-5 + t)(1 + -1t)) = 0

Ignore the factor 13.
Subproblem 1
Set the factor '(-5 + t)' equal to zero and attempt to solve:

Simplifying
-5 + t = 0

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

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

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

Simplifying
t = 5
Subproblem 2
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
Solution
t = {5, 1}