(30t^2+t)-32(30t^2+t)+31=0

Solution for (30t^2+t)-32(30t^2+t)+31=0 equation:

Simplifying
(30t2 + t) + -32(30t2 + t) + 31 = 0

Reorder the terms:
(t + 30t2) + -32(30t2 + t) + 31 = 0

Remove parenthesis around (t + 30t2)
t + 30t2 + -32(30t2 + t) + 31 = 0

Reorder the terms:
t + 30t2 + -32(t + 30t2) + 31 = 0
t + 30t2 + (t * -32 + 30t2 * -32) + 31 = 0
t + 30t2 + (-32t + -960t2) + 31 = 0

Reorder the terms:
31 + t + -32t + 30t2 + -960t2 = 0

Combine like terms: t + -32t = -31t
31 + -31t + 30t2 + -960t2 = 0

Combine like terms: 30t2 + -960t2 = -930t2
31 + -31t + -930t2 = 0

Solving
31 + -31t + -930t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '31'.
31(1 + -1t + -30t2) = 0

Factor a trinomial.
31((1 + -6t)(1 + 5t)) = 0

Ignore the factor 31.
Subproblem 1
Set the factor '(1 + -6t)' equal to zero and attempt to solve:

Simplifying
1 + -6t = 0

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

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

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

Divide each side by '-6'.
t = 0.1666666667

Simplifying
t = 0.1666666667
Subproblem 2
Set the factor '(1 + 5t)' equal to zero and attempt to solve:

Simplifying
1 + 5t = 0

Solving
1 + 5t = 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 + 5t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5t = 0 + -1
5t = 0 + -1

Combine like terms: 0 + -1 = -1
5t = -1

Divide each side by '5'.
t = -0.2

Simplifying
t = -0.2
Solution
t = {0.1666666667, -0.2}