(t-3)(t+5)=9

Solution for (t-3)(t+5)=9 equation:

Simplifying
(t + -3)(t + 5) = 9

Reorder the terms:
(-3 + t)(t + 5) = 9

Reorder the terms:
(-3 + t)(5 + t) = 9

Multiply (-3 + t) * (5 + t)
(-3(5 + t) + t(5 + t)) = 9
((5 * -3 + t * -3) + t(5 + t)) = 9
((-15 + -3t) + t(5 + t)) = 9
(-15 + -3t + (5 * t + t * t)) = 9
(-15 + -3t + (5t + t2)) = 9

Combine like terms: -3t + 5t = 2t
(-15 + 2t + t2) = 9

Solving
-15 + 2t + t2 = 9

Solving for variable 't'.

Reorder the terms:
-15 + -9 + 2t + t2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 2t + t2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 2t + t2 = 0

Factor a trinomial.
(-6 + -1t)(4 + -1t) = 0

Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
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 = {-6, 4}