(r+3)*(r-1)=(r+2)*(r-2)+3

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Solution for (r+3)*(r-1)=(r+2)*(r-2)+3 equation: 


Simplifying
(r + 3)(r + -1) = (r + 2)(r + -2) + 3

Reorder the terms:
(3 + r)(r + -1) = (r + 2)(r + -2) + 3

Reorder the terms:
(3 + r)(-1 + r) = (r + 2)(r + -2) + 3

Multiply (3 + r) * (-1 + r)
(3(-1 + r) + r(-1 + r)) = (r + 2)(r + -2) + 3
((-1 * 3 + r * 3) + r(-1 + r)) = (r + 2)(r + -2) + 3
((-3 + 3r) + r(-1 + r)) = (r + 2)(r + -2) + 3
(-3 + 3r + (-1 * r + r * r)) = (r + 2)(r + -2) + 3
(-3 + 3r + (-1r + r2)) = (r + 2)(r + -2) + 3

Combine like terms: 3r + -1r = 2r
(-3 + 2r + r2) = (r + 2)(r + -2) + 3

Reorder the terms:
-3 + 2r + r2 = (2 + r)(r + -2) + 3

Reorder the terms:
-3 + 2r + r2 = (2 + r)(-2 + r) + 3

Multiply (2 + r) * (-2 + r)
-3 + 2r + r2 = (2(-2 + r) + r(-2 + r)) + 3
-3 + 2r + r2 = ((-2 * 2 + r * 2) + r(-2 + r)) + 3
-3 + 2r + r2 = ((-4 + 2r) + r(-2 + r)) + 3
-3 + 2r + r2 = (-4 + 2r + (-2 * r + r * r)) + 3
-3 + 2r + r2 = (-4 + 2r + (-2r + r2)) + 3

Combine like terms: 2r + -2r = 0
-3 + 2r + r2 = (-4 + 0 + r2) + 3
-3 + 2r + r2 = (-4 + r2) + 3

Reorder the terms:
-3 + 2r + r2 = -4 + 3 + r2

Combine like terms: -4 + 3 = -1
-3 + 2r + r2 = -1 + r2

Add '-1r2' to each side of the equation.
-3 + 2r + r2 + -1r2 = -1 + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-3 + 2r + 0 = -1 + r2 + -1r2
-3 + 2r = -1 + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-3 + 2r = -1 + 0
-3 + 2r = -1

Solving
-3 + 2r = -1

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + 2r = -1 + 3

Combine like terms: -3 + 3 = 0
0 + 2r = -1 + 3
2r = -1 + 3

Combine like terms: -1 + 3 = 2
2r = 2

Divide each side by '2'.
r = 1

Simplifying
r = 1

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