2(r-5)(r-4)=(r-4)(r-3)+(r-2)(r-5)

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Solution for 2(r-5)(r-4)=(r-4)(r-3)+(r-2)(r-5) equation: 


Simplifying
2(r + -5)(r + -4) = (r + -4)(r + -3) + (r + -2)(r + -5)

Reorder the terms:
2(-5 + r)(r + -4) = (r + -4)(r + -3) + (r + -2)(r + -5)

Reorder the terms:
2(-5 + r)(-4 + r) = (r + -4)(r + -3) + (r + -2)(r + -5)

Multiply (-5 + r) * (-4 + r)
2(-5(-4 + r) + r(-4 + r)) = (r + -4)(r + -3) + (r + -2)(r + -5)
2((-4 * -5 + r * -5) + r(-4 + r)) = (r + -4)(r + -3) + (r + -2)(r + -5)
2((20 + -5r) + r(-4 + r)) = (r + -4)(r + -3) + (r + -2)(r + -5)
2(20 + -5r + (-4 * r + r * r)) = (r + -4)(r + -3) + (r + -2)(r + -5)
2(20 + -5r + (-4r + r2)) = (r + -4)(r + -3) + (r + -2)(r + -5)

Combine like terms: -5r + -4r = -9r
2(20 + -9r + r2) = (r + -4)(r + -3) + (r + -2)(r + -5)
(20 * 2 + -9r * 2 + r2 * 2) = (r + -4)(r + -3) + (r + -2)(r + -5)
(40 + -18r + 2r2) = (r + -4)(r + -3) + (r + -2)(r + -5)

Reorder the terms:
40 + -18r + 2r2 = (-4 + r)(r + -3) + (r + -2)(r + -5)

Reorder the terms:
40 + -18r + 2r2 = (-4 + r)(-3 + r) + (r + -2)(r + -5)

Multiply (-4 + r) * (-3 + r)
40 + -18r + 2r2 = (-4(-3 + r) + r(-3 + r)) + (r + -2)(r + -5)
40 + -18r + 2r2 = ((-3 * -4 + r * -4) + r(-3 + r)) + (r + -2)(r + -5)
40 + -18r + 2r2 = ((12 + -4r) + r(-3 + r)) + (r + -2)(r + -5)
40 + -18r + 2r2 = (12 + -4r + (-3 * r + r * r)) + (r + -2)(r + -5)
40 + -18r + 2r2 = (12 + -4r + (-3r + r2)) + (r + -2)(r + -5)

Combine like terms: -4r + -3r = -7r
40 + -18r + 2r2 = (12 + -7r + r2) + (r + -2)(r + -5)

Reorder the terms:
40 + -18r + 2r2 = 12 + -7r + r2 + (-2 + r)(r + -5)

Reorder the terms:
40 + -18r + 2r2 = 12 + -7r + r2 + (-2 + r)(-5 + r)

Multiply (-2 + r) * (-5 + r)
40 + -18r + 2r2 = 12 + -7r + r2 + (-2(-5 + r) + r(-5 + r))
40 + -18r + 2r2 = 12 + -7r + r2 + ((-5 * -2 + r * -2) + r(-5 + r))
40 + -18r + 2r2 = 12 + -7r + r2 + ((10 + -2r) + r(-5 + r))
40 + -18r + 2r2 = 12 + -7r + r2 + (10 + -2r + (-5 * r + r * r))
40 + -18r + 2r2 = 12 + -7r + r2 + (10 + -2r + (-5r + r2))

Combine like terms: -2r + -5r = -7r
40 + -18r + 2r2 = 12 + -7r + r2 + (10 + -7r + r2)

Reorder the terms:
40 + -18r + 2r2 = 12 + 10 + -7r + -7r + r2 + r2

Combine like terms: 12 + 10 = 22
40 + -18r + 2r2 = 22 + -7r + -7r + r2 + r2

Combine like terms: -7r + -7r = -14r
40 + -18r + 2r2 = 22 + -14r + r2 + r2

Combine like terms: r2 + r2 = 2r2
40 + -18r + 2r2 = 22 + -14r + 2r2

Add '-2r2' to each side of the equation.
40 + -18r + 2r2 + -2r2 = 22 + -14r + 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
40 + -18r + 0 = 22 + -14r + 2r2 + -2r2
40 + -18r = 22 + -14r + 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
40 + -18r = 22 + -14r + 0
40 + -18r = 22 + -14r

Solving
40 + -18r = 22 + -14r

Solving for variable 'r'.

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

Add '14r' to each side of the equation.
40 + -18r + 14r = 22 + -14r + 14r

Combine like terms: -18r + 14r = -4r
40 + -4r = 22 + -14r + 14r

Combine like terms: -14r + 14r = 0
40 + -4r = 22 + 0
40 + -4r = 22

Add '-40' to each side of the equation.
40 + -40 + -4r = 22 + -40

Combine like terms: 40 + -40 = 0
0 + -4r = 22 + -40
-4r = 22 + -40

Combine like terms: 22 + -40 = -18
-4r = -18

Divide each side by '-4'.
r = 4.5

Simplifying
r = 4.5

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