1(r-2)(r-6)=1+(r-4)(r-2)

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Solution for 1(r-2)(r-6)=1+(r-4)(r-2) equation: 


Simplifying
1(r + -2)(r + -6) = 1 + (r + -4)(r + -2)

Reorder the terms:
1(-2 + r)(r + -6) = 1 + (r + -4)(r + -2)

Reorder the terms:
1(-2 + r)(-6 + r) = 1 + (r + -4)(r + -2)

Multiply (-2 + r) * (-6 + r)
1(-2(-6 + r) + r(-6 + r)) = 1 + (r + -4)(r + -2)
1((-6 * -2 + r * -2) + r(-6 + r)) = 1 + (r + -4)(r + -2)
1((12 + -2r) + r(-6 + r)) = 1 + (r + -4)(r + -2)
1(12 + -2r + (-6 * r + r * r)) = 1 + (r + -4)(r + -2)
1(12 + -2r + (-6r + r2)) = 1 + (r + -4)(r + -2)

Combine like terms: -2r + -6r = -8r
1(12 + -8r + r2) = 1 + (r + -4)(r + -2)
(12 * 1 + -8r * 1 + r2 * 1) = 1 + (r + -4)(r + -2)
(12 + -8r + 1r2) = 1 + (r + -4)(r + -2)

Reorder the terms:
12 + -8r + 1r2 = 1 + (-4 + r)(r + -2)

Reorder the terms:
12 + -8r + 1r2 = 1 + (-4 + r)(-2 + r)

Multiply (-4 + r) * (-2 + r)
12 + -8r + 1r2 = 1 + (-4(-2 + r) + r(-2 + r))
12 + -8r + 1r2 = 1 + ((-2 * -4 + r * -4) + r(-2 + r))
12 + -8r + 1r2 = 1 + ((8 + -4r) + r(-2 + r))
12 + -8r + 1r2 = 1 + (8 + -4r + (-2 * r + r * r))
12 + -8r + 1r2 = 1 + (8 + -4r + (-2r + r2))

Combine like terms: -4r + -2r = -6r
12 + -8r + 1r2 = 1 + (8 + -6r + r2)

Combine like terms: 1 + 8 = 9
12 + -8r + 1r2 = 9 + -6r + r2

Solving
12 + -8r + 1r2 = 9 + -6r + r2

Solving for variable 'r'.

Reorder the terms:
12 + -9 + -8r + 6r + 1r2 + -1r2 = 9 + -6r + r2 + -9 + 6r + -1r2

Combine like terms: 12 + -9 = 3
3 + -8r + 6r + 1r2 + -1r2 = 9 + -6r + r2 + -9 + 6r + -1r2

Combine like terms: -8r + 6r = -2r
3 + -2r + 1r2 + -1r2 = 9 + -6r + r2 + -9 + 6r + -1r2

Combine like terms: 1r2 + -1r2 = 0
3 + -2r + 0 = 9 + -6r + r2 + -9 + 6r + -1r2
3 + -2r = 9 + -6r + r2 + -9 + 6r + -1r2

Reorder the terms:
3 + -2r = 9 + -9 + -6r + 6r + r2 + -1r2

Combine like terms: 9 + -9 = 0
3 + -2r = 0 + -6r + 6r + r2 + -1r2
3 + -2r = -6r + 6r + r2 + -1r2

Combine like terms: -6r + 6r = 0
3 + -2r = 0 + r2 + -1r2
3 + -2r = r2 + -1r2

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

The solution to this equation could not be determined.

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