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

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


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

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

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

Multiply (-3 + r) * (5 + r)
(-3(5 + r) + r(5 + r)) + (r + -3)(r + 2) = 0
((5 * -3 + r * -3) + r(5 + r)) + (r + -3)(r + 2) = 0
((-15 + -3r) + r(5 + r)) + (r + -3)(r + 2) = 0
(-15 + -3r + (5 * r + r * r)) + (r + -3)(r + 2) = 0
(-15 + -3r + (5r + r2)) + (r + -3)(r + 2) = 0

Combine like terms: -3r + 5r = 2r
(-15 + 2r + r2) + (r + -3)(r + 2) = 0

Reorder the terms:
-15 + 2r + r2 + (-3 + r)(r + 2) = 0

Reorder the terms:
-15 + 2r + r2 + (-3 + r)(2 + r) = 0

Multiply (-3 + r) * (2 + r)
-15 + 2r + r2 + (-3(2 + r) + r(2 + r)) = 0
-15 + 2r + r2 + ((2 * -3 + r * -3) + r(2 + r)) = 0
-15 + 2r + r2 + ((-6 + -3r) + r(2 + r)) = 0
-15 + 2r + r2 + (-6 + -3r + (2 * r + r * r)) = 0
-15 + 2r + r2 + (-6 + -3r + (2r + r2)) = 0

Combine like terms: -3r + 2r = -1r
-15 + 2r + r2 + (-6 + -1r + r2) = 0

Reorder the terms:
-15 + -6 + 2r + -1r + r2 + r2 = 0

Combine like terms: -15 + -6 = -21
-21 + 2r + -1r + r2 + r2 = 0

Combine like terms: 2r + -1r = 1r
-21 + 1r + r2 + r2 = 0

Combine like terms: r2 + r2 = 2r2
-21 + 1r + 2r2 = 0

Solving
-21 + 1r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -2r)(3 + -1r) = 0

Subproblem 1

Set the factor '(-7 + -2r)' equal to zero and attempt to solve: Simplifying -7 + -2r = 0 Solving -7 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2r = 0 + 7 -2r = 0 + 7 Combine like terms: 0 + 7 = 7 -2r = 7 Divide each side by '-2'. r = -3.5 Simplifying r = -3.5

Subproblem 2

Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Solution

r = {-3.5, 3}

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