(t-9)(t-4)=t-9

Solution for (t-9)(t-4)=t-9 equation:

Simplifying
(t + -9)(t + -4) = t + -9

Reorder the terms:
(-9 + t)(t + -4) = t + -9

Reorder the terms:
(-9 + t)(-4 + t) = t + -9

Multiply (-9 + t) * (-4 + t)
(-9(-4 + t) + t(-4 + t)) = t + -9
((-4 * -9 + t * -9) + t(-4 + t)) = t + -9
((36 + -9t) + t(-4 + t)) = t + -9
(36 + -9t + (-4 * t + t * t)) = t + -9
(36 + -9t + (-4t + t2)) = t + -9

Combine like terms: -9t + -4t = -13t
(36 + -13t + t2) = t + -9

Reorder the terms:
36 + -13t + t2 = -9 + t

Solving
36 + -13t + t2 = -9 + t

Solving for variable 't'.

Reorder the terms:
36 + 9 + -13t + -1t + t2 = -9 + t + 9 + -1t

Combine like terms: 36 + 9 = 45
45 + -13t + -1t + t2 = -9 + t + 9 + -1t

Combine like terms: -13t + -1t = -14t
45 + -14t + t2 = -9 + t + 9 + -1t

Reorder the terms:
45 + -14t + t2 = -9 + 9 + t + -1t

Combine like terms: -9 + 9 = 0
45 + -14t + t2 = 0 + t + -1t
45 + -14t + t2 = t + -1t

Combine like terms: t + -1t = 0
45 + -14t + t2 = 0

Factor a trinomial.
(5 + -1t)(9 + -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 '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {5, 9}