142=11t^2+t+40

Solution for 142=11t^2+t+40 equation:

Simplifying
142 = 11t2 + t + 40

Reorder the terms:
142 = 40 + t + 11t2

Solving
142 = 40 + t + 11t2

Solving for variable 't'.

Combine like terms: 142 + -40 = 102
102 + -1t + -11t2 = 40 + t + 11t2 + -40 + -1t + -11t2

Reorder the terms:
102 + -1t + -11t2 = 40 + -40 + t + -1t + 11t2 + -11t2

Combine like terms: 40 + -40 = 0
102 + -1t + -11t2 = 0 + t + -1t + 11t2 + -11t2
102 + -1t + -11t2 = t + -1t + 11t2 + -11t2

Combine like terms: t + -1t = 0
102 + -1t + -11t2 = 0 + 11t2 + -11t2
102 + -1t + -11t2 = 11t2 + -11t2

Combine like terms: 11t2 + -11t2 = 0
102 + -1t + -11t2 = 0

Factor a trinomial.
(3 + -1t)(34 + 11t) = 0

Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Subproblem 2
Set the factor '(34 + 11t)' equal to zero and attempt to solve:

Simplifying
34 + 11t = 0

Solving
34 + 11t = 0

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

Add '-34' to each side of the equation.
34 + -34 + 11t = 0 + -34

Combine like terms: 34 + -34 = 0
0 + 11t = 0 + -34
11t = 0 + -34

Combine like terms: 0 + -34 = -34
11t = -34

Divide each side by '11'.
t = -3.090909091

Simplifying
t = -3.090909091
Solution
t = {3, -3.090909091}