(t-1)(t-1)=(t+6)(t-7)+8

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Solution for (t-1)(t-1)=(t+6)(t-7)+8 equation:


Simplifying
(t + -1)(t + -1) = (t + 6)(t + -7) + 8

Reorder the terms:
(-1 + t)(t + -1) = (t + 6)(t + -7) + 8

Reorder the terms:
(-1 + t)(-1 + t) = (t + 6)(t + -7) + 8

Multiply (-1 + t) * (-1 + t)
(-1(-1 + t) + t(-1 + t)) = (t + 6)(t + -7) + 8
((-1 * -1 + t * -1) + t(-1 + t)) = (t + 6)(t + -7) + 8
((1 + -1t) + t(-1 + t)) = (t + 6)(t + -7) + 8
(1 + -1t + (-1 * t + t * t)) = (t + 6)(t + -7) + 8
(1 + -1t + (-1t + t2)) = (t + 6)(t + -7) + 8

Combine like terms: -1t + -1t = -2t
(1 + -2t + t2) = (t + 6)(t + -7) + 8

Reorder the terms:
1 + -2t + t2 = (6 + t)(t + -7) + 8

Reorder the terms:
1 + -2t + t2 = (6 + t)(-7 + t) + 8

Multiply (6 + t) * (-7 + t)
1 + -2t + t2 = (6(-7 + t) + t(-7 + t)) + 8
1 + -2t + t2 = ((-7 * 6 + t * 6) + t(-7 + t)) + 8
1 + -2t + t2 = ((-42 + 6t) + t(-7 + t)) + 8
1 + -2t + t2 = (-42 + 6t + (-7 * t + t * t)) + 8
1 + -2t + t2 = (-42 + 6t + (-7t + t2)) + 8

Combine like terms: 6t + -7t = -1t
1 + -2t + t2 = (-42 + -1t + t2) + 8

Reorder the terms:
1 + -2t + t2 = -42 + 8 + -1t + t2

Combine like terms: -42 + 8 = -34
1 + -2t + t2 = -34 + -1t + t2

Add '-1t2' to each side of the equation.
1 + -2t + t2 + -1t2 = -34 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
1 + -2t + 0 = -34 + -1t + t2 + -1t2
1 + -2t = -34 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
1 + -2t = -34 + -1t + 0
1 + -2t = -34 + -1t

Solving
1 + -2t = -34 + -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.
1 + -2t + t = -34 + -1t + t

Combine like terms: -2t + t = -1t
1 + -1t = -34 + -1t + t

Combine like terms: -1t + t = 0
1 + -1t = -34 + 0
1 + -1t = -34

Add '-1' to each side of the equation.
1 + -1 + -1t = -34 + -1

Combine like terms: 1 + -1 = 0
0 + -1t = -34 + -1
-1t = -34 + -1

Combine like terms: -34 + -1 = -35
-1t = -35

Divide each side by '-1'.
t = 35

Simplifying
t = 35

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