(t-5)(t+2)=

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

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

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

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

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

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

Solving
-10 + -3t + t2 = 0

Solving for variable 't'.

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