(T-4)(T+5)=

Solution for (T-4)(T+5)= equation:

Simplifying
(T + -4)(T + 5) = 0

Reorder the terms:
(-4 + T)(T + 5) = 0

Reorder the terms:
(-4 + T)(5 + T) = 0

Multiply (-4 + T) * (5 + T)
(-4(5 + T) + T(5 + T)) = 0
((5 * -4 + T * -4) + T(5 + T)) = 0
((-20 + -4T) + T(5 + T)) = 0
(-20 + -4T + (5 * T + T * T)) = 0
(-20 + -4T + (5T + T2)) = 0

Combine like terms: -4T + 5T = 1T
(-20 + 1T + T2) = 0

Solving
-20 + 1T + T2 = 0

Solving for variable 'T'.

Factor a trinomial.
(-5 + -1T)(4 + -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 '(4 + -1T)' equal to zero and attempt to solve:

Simplifying
4 + -1T = 0

Solving
4 + -1T = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1T = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1T = 0 + -4
-1T = 0 + -4

Combine like terms: 0 + -4 = -4
-1T = -4

Divide each side by '-1'.
T = 4

Simplifying
T = 4
Solution
T = {-5, 4}