(t+2)(t-2)=(t+3)(t-4)+6

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Solution for (t+2)(t-2)=(t+3)(t-4)+6 equation: 


Simplifying
(t + 2)(t + -2) = (t + 3)(t + -4) + 6

Reorder the terms:
(2 + t)(t + -2) = (t + 3)(t + -4) + 6

Reorder the terms:
(2 + t)(-2 + t) = (t + 3)(t + -4) + 6

Multiply (2 + t) * (-2 + t)
(2(-2 + t) + t(-2 + t)) = (t + 3)(t + -4) + 6
((-2 * 2 + t * 2) + t(-2 + t)) = (t + 3)(t + -4) + 6
((-4 + 2t) + t(-2 + t)) = (t + 3)(t + -4) + 6
(-4 + 2t + (-2 * t + t * t)) = (t + 3)(t + -4) + 6
(-4 + 2t + (-2t + t2)) = (t + 3)(t + -4) + 6

Combine like terms: 2t + -2t = 0
(-4 + 0 + t2) = (t + 3)(t + -4) + 6
(-4 + t2) = (t + 3)(t + -4) + 6

Reorder the terms:
-4 + t2 = (3 + t)(t + -4) + 6

Reorder the terms:
-4 + t2 = (3 + t)(-4 + t) + 6

Multiply (3 + t) * (-4 + t)
-4 + t2 = (3(-4 + t) + t(-4 + t)) + 6
-4 + t2 = ((-4 * 3 + t * 3) + t(-4 + t)) + 6
-4 + t2 = ((-12 + 3t) + t(-4 + t)) + 6
-4 + t2 = (-12 + 3t + (-4 * t + t * t)) + 6
-4 + t2 = (-12 + 3t + (-4t + t2)) + 6

Combine like terms: 3t + -4t = -1t
-4 + t2 = (-12 + -1t + t2) + 6

Reorder the terms:
-4 + t2 = -12 + 6 + -1t + t2

Combine like terms: -12 + 6 = -6
-4 + t2 = -6 + -1t + t2

Add '-1t2' to each side of the equation.
-4 + t2 + -1t2 = -6 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 + 0 = -6 + -1t + t2 + -1t2
-4 = -6 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 = -6 + -1t + 0
-4 = -6 + -1t

Solving
-4 = -6 + -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.
-4 + t = -6 + -1t + t

Combine like terms: -1t + t = 0
-4 + t = -6 + 0
-4 + t = -6

Add '4' to each side of the equation.
-4 + 4 + t = -6 + 4

Combine like terms: -4 + 4 = 0
0 + t = -6 + 4
t = -6 + 4

Combine like terms: -6 + 4 = -2
t = -2

Simplifying
t = -2

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