0=10-t-3t^2

Solution for 0=10-t-3t^2 equation:

Simplifying
0 = 10 + -1t + -3t2

Solving
0 = 10 + -1t + -3t2

Solving for variable 't'.

Combine like terms: 0 + -10 = -10
-10 + t + 3t2 = 10 + -1t + -3t2 + -10 + t + 3t2

Reorder the terms:
-10 + t + 3t2 = 10 + -10 + -1t + t + -3t2 + 3t2

Combine like terms: 10 + -10 = 0
-10 + t + 3t2 = 0 + -1t + t + -3t2 + 3t2
-10 + t + 3t2 = -1t + t + -3t2 + 3t2

Combine like terms: -1t + t = 0
-10 + t + 3t2 = 0 + -3t2 + 3t2
-10 + t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-10 + t + 3t2 = 0

Factor a trinomial.
(-2 + -1t)(5 + -3t) = 0

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve:

Simplifying
5 + -3t = 0

Solving
5 + -3t = 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 + -3t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3t = 0 + -5
-3t = 0 + -5

Combine like terms: 0 + -5 = -5
-3t = -5

Divide each side by '-3'.
t = 1.666666667

Simplifying
t = 1.666666667
Solution
t = {-2, 1.666666667}