49t^2-245*t-294=0

Solution for 49t^2-245*t-294=0 equation:

Simplifying
49t2 + -245t + -294 = 0

Reorder the terms:
-294 + -245t + 49t2 = 0

Solving
-294 + -245t + 49t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '49'.
49(-6 + -5t + t2) = 0

Factor a trinomial.
49((-1 + -1t)(6 + -1t)) = 0

Ignore the factor 49.
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}