(t-14)(t+1)=0

Solution for (t-14)(t+1)=0 equation:

Simplifying
(t + -14)(t + 1) = 0

Reorder the terms:
(-14 + t)(t + 1) = 0

Reorder the terms:
(-14 + t)(1 + t) = 0

Multiply (-14 + t) * (1 + t)
(-14(1 + t) + t(1 + t)) = 0
((1 * -14 + t * -14) + t(1 + t)) = 0
((-14 + -14t) + t(1 + t)) = 0
(-14 + -14t + (1 * t + t * t)) = 0
(-14 + -14t + (1t + t2)) = 0

Combine like terms: -14t + 1t = -13t
(-14 + -13t + t2) = 0

Solving
-14 + -13t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -1t)(14 + -1t) = 0

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

Simplifying
-1 + -1t = 0

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

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(14 + -1t)' equal to zero and attempt to solve:

Simplifying
14 + -1t = 0

Solving
14 + -1t = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1t = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1t = 0 + -14
-1t = 0 + -14

Combine like terms: 0 + -14 = -14
-1t = -14

Divide each side by '-1'.
t = 14

Simplifying
t = 14
Solution
t = {-1, 14}