(t+1)(t-1)=(t+3)(t-4)+7

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Solution for (t+1)(t-1)=(t+3)(t-4)+7 equation: 


Simplifying
(t + 1)(t + -1) = (t + 3)(t + -4) + 7

Reorder the terms:
(1 + t)(t + -1) = (t + 3)(t + -4) + 7

Reorder the terms:
(1 + t)(-1 + t) = (t + 3)(t + -4) + 7

Multiply (1 + t) * (-1 + t)
(1(-1 + t) + t(-1 + t)) = (t + 3)(t + -4) + 7
((-1 * 1 + t * 1) + t(-1 + t)) = (t + 3)(t + -4) + 7
((-1 + 1t) + t(-1 + t)) = (t + 3)(t + -4) + 7
(-1 + 1t + (-1 * t + t * t)) = (t + 3)(t + -4) + 7
(-1 + 1t + (-1t + t2)) = (t + 3)(t + -4) + 7

Combine like terms: 1t + -1t = 0
(-1 + 0 + t2) = (t + 3)(t + -4) + 7
(-1 + t2) = (t + 3)(t + -4) + 7

Reorder the terms:
-1 + t2 = (3 + t)(t + -4) + 7

Reorder the terms:
-1 + t2 = (3 + t)(-4 + t) + 7

Multiply (3 + t) * (-4 + t)
-1 + t2 = (3(-4 + t) + t(-4 + t)) + 7
-1 + t2 = ((-4 * 3 + t * 3) + t(-4 + t)) + 7
-1 + t2 = ((-12 + 3t) + t(-4 + t)) + 7
-1 + t2 = (-12 + 3t + (-4 * t + t * t)) + 7
-1 + t2 = (-12 + 3t + (-4t + t2)) + 7

Combine like terms: 3t + -4t = -1t
-1 + t2 = (-12 + -1t + t2) + 7

Reorder the terms:
-1 + t2 = -12 + 7 + -1t + t2

Combine like terms: -12 + 7 = -5
-1 + t2 = -5 + -1t + t2

Add '-1t2' to each side of the equation.
-1 + t2 + -1t2 = -5 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-1 + 0 = -5 + -1t + t2 + -1t2
-1 = -5 + -1t + t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-1 = -5 + -1t + 0
-1 = -5 + -1t

Solving
-1 = -5 + -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 + t = -5 + -1t + t

Combine like terms: -1t + t = 0
-1 + t = -5 + 0
-1 + t = -5

Add '1' to each side of the equation.
-1 + 1 + t = -5 + 1

Combine like terms: -1 + 1 = 0
0 + t = -5 + 1
t = -5 + 1

Combine like terms: -5 + 1 = -4
t = -4

Simplifying
t = -4

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