0=t^2-3t-10

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

Simplifying
0 = t2 + -3t + -10

Reorder the terms:
0 = -10 + -3t + t2

Solving
0 = -10 + -3t + t2

Solving for variable 't'.

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

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

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

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

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

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

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

Simplifying
5 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 5

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

Simplifying
2 + t = 0

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

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

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

Simplifying
t = -2
Solution
t = {5, -2}