(r-6)(r-2)=(r-4)(r-5)

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Solution for (r-6)(r-2)=(r-4)(r-5) equation: 


Simplifying
(r + -6)(r + -2) = (r + -4)(r + -5)

Reorder the terms:
(-6 + r)(r + -2) = (r + -4)(r + -5)

Reorder the terms:
(-6 + r)(-2 + r) = (r + -4)(r + -5)

Multiply (-6 + r) * (-2 + r)
(-6(-2 + r) + r(-2 + r)) = (r + -4)(r + -5)
((-2 * -6 + r * -6) + r(-2 + r)) = (r + -4)(r + -5)
((12 + -6r) + r(-2 + r)) = (r + -4)(r + -5)
(12 + -6r + (-2 * r + r * r)) = (r + -4)(r + -5)
(12 + -6r + (-2r + r2)) = (r + -4)(r + -5)

Combine like terms: -6r + -2r = -8r
(12 + -8r + r2) = (r + -4)(r + -5)

Reorder the terms:
12 + -8r + r2 = (-4 + r)(r + -5)

Reorder the terms:
12 + -8r + r2 = (-4 + r)(-5 + r)

Multiply (-4 + r) * (-5 + r)
12 + -8r + r2 = (-4(-5 + r) + r(-5 + r))
12 + -8r + r2 = ((-5 * -4 + r * -4) + r(-5 + r))
12 + -8r + r2 = ((20 + -4r) + r(-5 + r))
12 + -8r + r2 = (20 + -4r + (-5 * r + r * r))
12 + -8r + r2 = (20 + -4r + (-5r + r2))

Combine like terms: -4r + -5r = -9r
12 + -8r + r2 = (20 + -9r + r2)

Add '-1r2' to each side of the equation.
12 + -8r + r2 + -1r2 = 20 + -9r + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
12 + -8r + 0 = 20 + -9r + r2 + -1r2
12 + -8r = 20 + -9r + r2 + -1r2

Combine like terms: r2 + -1r2 = 0
12 + -8r = 20 + -9r + 0
12 + -8r = 20 + -9r

Solving
12 + -8r = 20 + -9r

Solving for variable 'r'.

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

Add '9r' to each side of the equation.
12 + -8r + 9r = 20 + -9r + 9r

Combine like terms: -8r + 9r = 1r
12 + 1r = 20 + -9r + 9r

Combine like terms: -9r + 9r = 0
12 + 1r = 20 + 0
12 + 1r = 20

Add '-12' to each side of the equation.
12 + -12 + 1r = 20 + -12

Combine like terms: 12 + -12 = 0
0 + 1r = 20 + -12
1r = 20 + -12

Combine like terms: 20 + -12 = 8
1r = 8

Divide each side by '1'.
r = 8

Simplifying
r = 8

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