(t-14)(t+6)=t-14

Solution for (t-14)(t+6)=t-14 equation:

Simplifying
(t + -14)(t + 6) = t + -14

Reorder the terms:
(-14 + t)(t + 6) = t + -14

Reorder the terms:
(-14 + t)(6 + t) = t + -14

Multiply (-14 + t) * (6 + t)
(-14(6 + t) + t(6 + t)) = t + -14
((6 * -14 + t * -14) + t(6 + t)) = t + -14
((-84 + -14t) + t(6 + t)) = t + -14
(-84 + -14t + (6 * t + t * t)) = t + -14
(-84 + -14t + (6t + t2)) = t + -14

Combine like terms: -14t + 6t = -8t
(-84 + -8t + t2) = t + -14

Reorder the terms:
-84 + -8t + t2 = -14 + t

Solving
-84 + -8t + t2 = -14 + t

Solving for variable 't'.

Reorder the terms:
-84 + 14 + -8t + -1t + t2 = -14 + t + 14 + -1t

Combine like terms: -84 + 14 = -70
-70 + -8t + -1t + t2 = -14 + t + 14 + -1t

Combine like terms: -8t + -1t = -9t
-70 + -9t + t2 = -14 + t + 14 + -1t

Reorder the terms:
-70 + -9t + t2 = -14 + 14 + t + -1t

Combine like terms: -14 + 14 = 0
-70 + -9t + t2 = 0 + t + -1t
-70 + -9t + t2 = t + -1t

Combine like terms: t + -1t = 0
-70 + -9t + t2 = 0

Factor a trinomial.
(-5 + -1t)(14 + -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 '(14 + -1t)' equal to zero and attempt to solve:

Simplifying
14 + -1t = 0

Solving
14 + -1t = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1t = 0 + -14

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

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

Divide each side by '-1'.
t = 14

Simplifying
t = 14
Solution
t = {-5, 14}