6t^2+t-35=0

Solution for 6t^2+t-35=0 equation:

Simplifying
6t2 + t + -35 = 0

Reorder the terms:
-35 + t + 6t2 = 0

Solving
-35 + t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -2t)(7 + -3t) = 0

Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve:

Simplifying
-5 + -2t = 0

Solving
-5 + -2t = 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 + -2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t = 0 + 5
-2t = 0 + 5

Combine like terms: 0 + 5 = 5
-2t = 5

Divide each side by '-2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
Set the factor '(7 + -3t)' equal to zero and attempt to solve:

Simplifying
7 + -3t = 0

Solving
7 + -3t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3t = 0 + -7
-3t = 0 + -7

Combine like terms: 0 + -7 = -7
-3t = -7

Divide each side by '-3'.
t = 2.333333333

Simplifying
t = 2.333333333
Solution
t = {-2.5, 2.333333333}