(t-12)(t+2)=t-12

Solution for (t-12)(t+2)=t-12 equation:

Simplifying
(t + -12)(t + 2) = t + -12

Reorder the terms:
(-12 + t)(t + 2) = t + -12

Reorder the terms:
(-12 + t)(2 + t) = t + -12

Multiply (-12 + t) * (2 + t)
(-12(2 + t) + t(2 + t)) = t + -12
((2 * -12 + t * -12) + t(2 + t)) = t + -12
((-24 + -12t) + t(2 + t)) = t + -12
(-24 + -12t + (2 * t + t * t)) = t + -12
(-24 + -12t + (2t + t2)) = t + -12

Combine like terms: -12t + 2t = -10t
(-24 + -10t + t2) = t + -12

Reorder the terms:
-24 + -10t + t2 = -12 + t

Solving
-24 + -10t + t2 = -12 + t

Solving for variable 't'.

Reorder the terms:
-24 + 12 + -10t + -1t + t2 = -12 + t + 12 + -1t

Combine like terms: -24 + 12 = -12
-12 + -10t + -1t + t2 = -12 + t + 12 + -1t

Combine like terms: -10t + -1t = -11t
-12 + -11t + t2 = -12 + t + 12 + -1t

Reorder the terms:
-12 + -11t + t2 = -12 + 12 + t + -1t

Combine like terms: -12 + 12 = 0
-12 + -11t + t2 = 0 + t + -1t
-12 + -11t + t2 = t + -1t

Combine like terms: t + -1t = 0
-12 + -11t + t2 = 0

Factor a trinomial.
(-1 + -1t)(12 + -1t) = 0

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

Simplifying
-1 + -1t = 0

Solving
-1 + -1t = 0

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

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

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

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

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

Simplifying
t = -1
Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {-1, 12}