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

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


Simplifying
2(r + -2)(r + -5) + -1(r + 4)(2r + -6) = 0

Reorder the terms:
2(-2 + r)(r + -5) + -1(r + 4)(2r + -6) = 0

Reorder the terms:
2(-2 + r)(-5 + r) + -1(r + 4)(2r + -6) = 0

Multiply (-2 + r) * (-5 + r)
2(-2(-5 + r) + r(-5 + r)) + -1(r + 4)(2r + -6) = 0
2((-5 * -2 + r * -2) + r(-5 + r)) + -1(r + 4)(2r + -6) = 0
2((10 + -2r) + r(-5 + r)) + -1(r + 4)(2r + -6) = 0
2(10 + -2r + (-5 * r + r * r)) + -1(r + 4)(2r + -6) = 0
2(10 + -2r + (-5r + r2)) + -1(r + 4)(2r + -6) = 0

Combine like terms: -2r + -5r = -7r
2(10 + -7r + r2) + -1(r + 4)(2r + -6) = 0
(10 * 2 + -7r * 2 + r2 * 2) + -1(r + 4)(2r + -6) = 0
(20 + -14r + 2r2) + -1(r + 4)(2r + -6) = 0

Reorder the terms:
20 + -14r + 2r2 + -1(4 + r)(2r + -6) = 0

Reorder the terms:
20 + -14r + 2r2 + -1(4 + r)(-6 + 2r) = 0

Multiply (4 + r) * (-6 + 2r)
20 + -14r + 2r2 + -1(4(-6 + 2r) + r(-6 + 2r)) = 0
20 + -14r + 2r2 + -1((-6 * 4 + 2r * 4) + r(-6 + 2r)) = 0
20 + -14r + 2r2 + -1((-24 + 8r) + r(-6 + 2r)) = 0
20 + -14r + 2r2 + -1(-24 + 8r + (-6 * r + 2r * r)) = 0
20 + -14r + 2r2 + -1(-24 + 8r + (-6r + 2r2)) = 0

Combine like terms: 8r + -6r = 2r
20 + -14r + 2r2 + -1(-24 + 2r + 2r2) = 0
20 + -14r + 2r2 + (-24 * -1 + 2r * -1 + 2r2 * -1) = 0
20 + -14r + 2r2 + (24 + -2r + -2r2) = 0

Reorder the terms:
20 + 24 + -14r + -2r + 2r2 + -2r2 = 0

Combine like terms: 20 + 24 = 44
44 + -14r + -2r + 2r2 + -2r2 = 0

Combine like terms: -14r + -2r = -16r
44 + -16r + 2r2 + -2r2 = 0

Combine like terms: 2r2 + -2r2 = 0
44 + -16r + 0 = 0
44 + -16r = 0

Solving
44 + -16r = 0

Solving for variable 'r'.

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

Add '-44' to each side of the equation.
44 + -44 + -16r = 0 + -44

Combine like terms: 44 + -44 = 0
0 + -16r = 0 + -44
-16r = 0 + -44

Combine like terms: 0 + -44 = -44
-16r = -44

Divide each side by '-16'.
r = 2.75

Simplifying
r = 2.75

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