0=t^2-2t-35

Solution for 0=t^2-2t-35 equation:

Simplifying
0 = t2 + -2t + -35

Reorder the terms:
0 = -35 + -2t + t2

Solving
0 = -35 + -2t + t2

Solving for variable 't'.

Combine like terms: 0 + 35 = 35
35 + 2t + -1t2 = -35 + -2t + t2 + 35 + 2t + -1t2

Reorder the terms:
35 + 2t + -1t2 = -35 + 35 + -2t + 2t + t2 + -1t2

Combine like terms: -35 + 35 = 0
35 + 2t + -1t2 = 0 + -2t + 2t + t2 + -1t2
35 + 2t + -1t2 = -2t + 2t + t2 + -1t2

Combine like terms: -2t + 2t = 0
35 + 2t + -1t2 = 0 + t2 + -1t2
35 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
35 + 2t + -1t2 = 0

Factor a trinomial.
(7 + -1t)(5 + t) = 0

Subproblem 1
Set the factor '(7 + -1t)' equal to zero and attempt to solve:

Simplifying
7 + -1t = 0

Solving
7 + -1t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1t = 0 + -7
-1t = 0 + -7

Combine like terms: 0 + -7 = -7
-1t = -7

Divide each side by '-1'.
t = 7

Simplifying
t = 7
Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

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

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

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

Simplifying
t = -5
Solution
t = {7, -5}