(t-2)(t+5)=0

Solution for (t-2)(t+5)=0 equation:

Simplifying
(t + -2)(t + 5) = 0

Reorder the terms:
(-2 + t)(t + 5) = 0

Reorder the terms:
(-2 + t)(5 + t) = 0

Multiply (-2 + t) * (5 + t)
(-2(5 + t) + t(5 + t)) = 0
((5 * -2 + t * -2) + t(5 + t)) = 0
((-10 + -2t) + t(5 + t)) = 0
(-10 + -2t + (5 * t + t * t)) = 0
(-10 + -2t + (5t + t2)) = 0

Combine like terms: -2t + 5t = 3t
(-10 + 3t + t2) = 0

Solving
-10 + 3t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -1t)(2 + -1t) = 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 + -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
Solution
t = {-5, 2}