5t^2+t-6=0

Solution for 5t^2+t-6=0 equation:

Simplifying
5t2 + t + -6 = 0

Reorder the terms:
-6 + t + 5t2 = 0

Solving
-6 + t + 5t2 = 0

Solving for variable 't'.

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

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

Simplifying
-6 + -5t = 0

Solving
-6 + -5t = 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 + -5t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5t = 0 + 6
-5t = 0 + 6

Combine like terms: 0 + 6 = 6
-5t = 6

Divide each side by '-5'.
t = -1.2

Simplifying
t = -1.2
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 = {-1.2, 1}