(t+2)(t-2)=(t+6)(t-7)+9

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Solution for (t+2)(t-2)=(t+6)(t-7)+9 equation:


Simplifying
(t + 2)(t + -2) = (t + 6)(t + -7) + 9

Reorder the terms:
(2 + t)(t + -2) = (t + 6)(t + -7) + 9

Reorder the terms:
(2 + t)(-2 + t) = (t + 6)(t + -7) + 9

Multiply (2 + t) * (-2 + t)
(2(-2 + t) + t(-2 + t)) = (t + 6)(t + -7) + 9
((-2 * 2 + t * 2) + t(-2 + t)) = (t + 6)(t + -7) + 9
((-4 + 2t) + t(-2 + t)) = (t + 6)(t + -7) + 9
(-4 + 2t + (-2 * t + t * t)) = (t + 6)(t + -7) + 9
(-4 + 2t + (-2t + t2)) = (t + 6)(t + -7) + 9

Combine like terms: 2t + -2t = 0
(-4 + 0 + t2) = (t + 6)(t + -7) + 9
(-4 + t2) = (t + 6)(t + -7) + 9

Reorder the terms:
-4 + t2 = (6 + t)(t + -7) + 9

Reorder the terms:
-4 + t2 = (6 + t)(-7 + t) + 9

Multiply (6 + t) * (-7 + t)
-4 + t2 = (6(-7 + t) + t(-7 + t)) + 9
-4 + t2 = ((-7 * 6 + t * 6) + t(-7 + t)) + 9
-4 + t2 = ((-42 + 6t) + t(-7 + t)) + 9
-4 + t2 = (-42 + 6t + (-7 * t + t * t)) + 9
-4 + t2 = (-42 + 6t + (-7t + t2)) + 9

Combine like terms: 6t + -7t = -1t
-4 + t2 = (-42 + -1t + t2) + 9

Reorder the terms:
-4 + t2 = -42 + 9 + -1t + t2

Combine like terms: -42 + 9 = -33
-4 + t2 = -33 + -1t + t2

Add '-1t2' to each side of the equation.
-4 + t2 + -1t2 = -33 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 + 0 = -33 + -1t + t2 + -1t2
-4 = -33 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-4 = -33 + -1t + 0
-4 = -33 + -1t

Solving
-4 = -33 + -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 = -33 + -1t + t

Combine like terms: -1t + t = 0
-4 + t = -33 + 0
-4 + t = -33

Add '4' to each side of the equation.
-4 + 4 + t = -33 + 4

Combine like terms: -4 + 4 = 0
0 + t = -33 + 4
t = -33 + 4

Combine like terms: -33 + 4 = -29
t = -29

Simplifying
t = -29

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