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

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


Simplifying
(2x + 3)(3 + -1r) + -1(2x + -5)(3 + -1r) = 0

Reorder the terms:
(3 + 2x)(3 + -1r) + -1(2x + -5)(3 + -1r) = 0

Multiply (3 + 2x) * (3 + -1r)
(3(3 + -1r) + 2x * (3 + -1r)) + -1(2x + -5)(3 + -1r) = 0
((3 * 3 + -1r * 3) + 2x * (3 + -1r)) + -1(2x + -5)(3 + -1r) = 0
((9 + -3r) + 2x * (3 + -1r)) + -1(2x + -5)(3 + -1r) = 0
(9 + -3r + (3 * 2x + -1r * 2x)) + -1(2x + -5)(3 + -1r) = 0

Reorder the terms:
(9 + -3r + (-2rx + 6x)) + -1(2x + -5)(3 + -1r) = 0
(9 + -3r + (-2rx + 6x)) + -1(2x + -5)(3 + -1r) = 0
(9 + -3r + -2rx + 6x) + -1(2x + -5)(3 + -1r) = 0

Reorder the terms:
9 + -3r + -2rx + 6x + -1(-5 + 2x)(3 + -1r) = 0

Multiply (-5 + 2x) * (3 + -1r)
9 + -3r + -2rx + 6x + -1(-5(3 + -1r) + 2x * (3 + -1r)) = 0
9 + -3r + -2rx + 6x + -1((3 * -5 + -1r * -5) + 2x * (3 + -1r)) = 0
9 + -3r + -2rx + 6x + -1((-15 + 5r) + 2x * (3 + -1r)) = 0
9 + -3r + -2rx + 6x + -1(-15 + 5r + (3 * 2x + -1r * 2x)) = 0

Reorder the terms:
9 + -3r + -2rx + 6x + -1(-15 + 5r + (-2rx + 6x)) = 0
9 + -3r + -2rx + 6x + -1(-15 + 5r + (-2rx + 6x)) = 0
9 + -3r + -2rx + 6x + -1(-15 + 5r + -2rx + 6x) = 0
9 + -3r + -2rx + 6x + (-15 * -1 + 5r * -1 + -2rx * -1 + 6x * -1) = 0
9 + -3r + -2rx + 6x + (15 + -5r + 2rx + -6x) = 0

Reorder the terms:
9 + 15 + -3r + -5r + -2rx + 2rx + 6x + -6x = 0

Combine like terms: 9 + 15 = 24
24 + -3r + -5r + -2rx + 2rx + 6x + -6x = 0

Combine like terms: -3r + -5r = -8r
24 + -8r + -2rx + 2rx + 6x + -6x = 0

Combine like terms: -2rx + 2rx = 0
24 + -8r + 0 + 6x + -6x = 0
24 + -8r + 6x + -6x = 0

Combine like terms: 6x + -6x = 0
24 + -8r + 0 = 0
24 + -8r = 0

Solving
24 + -8r = 0

Solving for variable 'r'.

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

Add '-24' to each side of the equation.
24 + -24 + -8r = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -8r = 0 + -24
-8r = 0 + -24

Combine like terms: 0 + -24 = -24
-8r = -24

Divide each side by '-8'.
r = 3

Simplifying
r = 3

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