(t+6)(t-6)=(t+7)(t-8)+9

Solution for (t+6)(t-6)=(t+7)(t-8)+9 equation:

Simplifying
(t + 6)(t + -6) = (t + 7)(t + -8) + 9

Reorder the terms:
(6 + t)(t + -6) = (t + 7)(t + -8) + 9

Reorder the terms:
(6 + t)(-6 + t) = (t + 7)(t + -8) + 9

Multiply (6 + t) * (-6 + t)
(6(-6 + t) + t(-6 + t)) = (t + 7)(t + -8) + 9
((-6 * 6 + t * 6) + t(-6 + t)) = (t + 7)(t + -8) + 9
((-36 + 6t) + t(-6 + t)) = (t + 7)(t + -8) + 9
(-36 + 6t + (-6 * t + t * t)) = (t + 7)(t + -8) + 9
(-36 + 6t + (-6t + t2)) = (t + 7)(t + -8) + 9

Combine like terms: 6t + -6t = 0
(-36 + 0 + t2) = (t + 7)(t + -8) + 9
(-36 + t2) = (t + 7)(t + -8) + 9

Reorder the terms:
-36 + t2 = (7 + t)(t + -8) + 9

Reorder the terms:
-36 + t2 = (7 + t)(-8 + t) + 9

Multiply (7 + t) * (-8 + t)
-36 + t2 = (7(-8 + t) + t(-8 + t)) + 9
-36 + t2 = ((-8 * 7 + t * 7) + t(-8 + t)) + 9
-36 + t2 = ((-56 + 7t) + t(-8 + t)) + 9
-36 + t2 = (-56 + 7t + (-8 * t + t * t)) + 9
-36 + t2 = (-56 + 7t + (-8t + t2)) + 9

Combine like terms: 7t + -8t = -1t
-36 + t2 = (-56 + -1t + t2) + 9

Reorder the terms:
-36 + t2 = -56 + 9 + -1t + t2

Combine like terms: -56 + 9 = -47
-36 + t2 = -47 + -1t + t2

Add '-1t2' to each side of the equation.
-36 + t2 + -1t2 = -47 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-36 + 0 = -47 + -1t + t2 + -1t2
-36 = -47 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-36 = -47 + -1t + 0
-36 = -47 + -1t

Solving
-36 = -47 + -1t

Solving for variable 't'.

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

Add 't' to each side of the equation.
-36 + t = -47 + -1t + t

Combine like terms: -1t + t = 0
-36 + t = -47 + 0
-36 + t = -47

Add '36' to each side of the equation.
-36 + 36 + t = -47 + 36

Combine like terms: -36 + 36 = 0
0 + t = -47 + 36
t = -47 + 36

Combine like terms: -47 + 36 = -11
t = -11

Simplifying
t = -11