(t+3)(t-3)=(t+4)(t-5)+9

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Solution for (t+3)(t-3)=(t+4)(t-5)+9 equation: 


Simplifying
(t + 3)(t + -3) = (t + 4)(t + -5) + 9

Reorder the terms:
(3 + t)(t + -3) = (t + 4)(t + -5) + 9

Reorder the terms:
(3 + t)(-3 + t) = (t + 4)(t + -5) + 9

Multiply (3 + t) * (-3 + t)
(3(-3 + t) + t(-3 + t)) = (t + 4)(t + -5) + 9
((-3 * 3 + t * 3) + t(-3 + t)) = (t + 4)(t + -5) + 9
((-9 + 3t) + t(-3 + t)) = (t + 4)(t + -5) + 9
(-9 + 3t + (-3 * t + t * t)) = (t + 4)(t + -5) + 9
(-9 + 3t + (-3t + t2)) = (t + 4)(t + -5) + 9

Combine like terms: 3t + -3t = 0
(-9 + 0 + t2) = (t + 4)(t + -5) + 9
(-9 + t2) = (t + 4)(t + -5) + 9

Reorder the terms:
-9 + t2 = (4 + t)(t + -5) + 9

Reorder the terms:
-9 + t2 = (4 + t)(-5 + t) + 9

Multiply (4 + t) * (-5 + t)
-9 + t2 = (4(-5 + t) + t(-5 + t)) + 9
-9 + t2 = ((-5 * 4 + t * 4) + t(-5 + t)) + 9
-9 + t2 = ((-20 + 4t) + t(-5 + t)) + 9
-9 + t2 = (-20 + 4t + (-5 * t + t * t)) + 9
-9 + t2 = (-20 + 4t + (-5t + t2)) + 9

Combine like terms: 4t + -5t = -1t
-9 + t2 = (-20 + -1t + t2) + 9

Reorder the terms:
-9 + t2 = -20 + 9 + -1t + t2

Combine like terms: -20 + 9 = -11
-9 + t2 = -11 + -1t + t2

Add '-1t2' to each side of the equation.
-9 + t2 + -1t2 = -11 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-9 + 0 = -11 + -1t + t2 + -1t2
-9 = -11 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-9 = -11 + -1t + 0
-9 = -11 + -1t

Solving
-9 = -11 + -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.
-9 + t = -11 + -1t + t

Combine like terms: -1t + t = 0
-9 + t = -11 + 0
-9 + t = -11

Add '9' to each side of the equation.
-9 + 9 + t = -11 + 9

Combine like terms: -9 + 9 = 0
0 + t = -11 + 9
t = -11 + 9

Combine like terms: -11 + 9 = -2
t = -2

Simplifying
t = -2

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