(t+2)(t-2)=(t+5)(t-6)+7

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Solution for (t+2)(t-2)=(t+5)(t-6)+7 equation: 


Simplifying
(t + 2)(t + -2) = (t + 5)(t + -6) + 7

Reorder the terms:
(2 + t)(t + -2) = (t + 5)(t + -6) + 7

Reorder the terms:
(2 + t)(-2 + t) = (t + 5)(t + -6) + 7

Multiply (2 + t) * (-2 + t)
(2(-2 + t) + t(-2 + t)) = (t + 5)(t + -6) + 7
((-2 * 2 + t * 2) + t(-2 + t)) = (t + 5)(t + -6) + 7
((-4 + 2t) + t(-2 + t)) = (t + 5)(t + -6) + 7
(-4 + 2t + (-2 * t + t * t)) = (t + 5)(t + -6) + 7
(-4 + 2t + (-2t + t2)) = (t + 5)(t + -6) + 7

Combine like terms: 2t + -2t = 0
(-4 + 0 + t2) = (t + 5)(t + -6) + 7
(-4 + t2) = (t + 5)(t + -6) + 7

Reorder the terms:
-4 + t2 = (5 + t)(t + -6) + 7

Reorder the terms:
-4 + t2 = (5 + t)(-6 + t) + 7

Multiply (5 + t) * (-6 + t)
-4 + t2 = (5(-6 + t) + t(-6 + t)) + 7
-4 + t2 = ((-6 * 5 + t * 5) + t(-6 + t)) + 7
-4 + t2 = ((-30 + 5t) + t(-6 + t)) + 7
-4 + t2 = (-30 + 5t + (-6 * t + t * t)) + 7
-4 + t2 = (-30 + 5t + (-6t + t2)) + 7

Combine like terms: 5t + -6t = -1t
-4 + t2 = (-30 + -1t + t2) + 7

Reorder the terms:
-4 + t2 = -30 + 7 + -1t + t2

Combine like terms: -30 + 7 = -23
-4 + t2 = -23 + -1t + t2

Add '-1t2' to each side of the equation.
-4 + t2 + -1t2 = -23 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 + 0 = -23 + -1t + t2 + -1t2
-4 = -23 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 = -23 + -1t + 0
-4 = -23 + -1t

Solving
-4 = -23 + -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 = -23 + -1t + t

Combine like terms: -1t + t = 0
-4 + t = -23 + 0
-4 + t = -23

Add '4' to each side of the equation.
-4 + 4 + t = -23 + 4

Combine like terms: -4 + 4 = 0
0 + t = -23 + 4
t = -23 + 4

Combine like terms: -23 + 4 = -19
t = -19

Simplifying
t = -19

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