(13-2r)*(13-r)=24

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Solution for (13-2r)*(13-r)=24 equation:


Simplifying
(13 + -2r)(13 + -1r) = 24

Multiply (13 + -2r) * (13 + -1r)
(13(13 + -1r) + -2r * (13 + -1r)) = 24
((13 * 13 + -1r * 13) + -2r * (13 + -1r)) = 24
((169 + -13r) + -2r * (13 + -1r)) = 24
(169 + -13r + (13 * -2r + -1r * -2r)) = 24
(169 + -13r + (-26r + 2r2)) = 24

Combine like terms: -13r + -26r = -39r
(169 + -39r + 2r2) = 24

Solving
169 + -39r + 2r2 = 24

Solving for variable 'r'.

Reorder the terms:
169 + -24 + -39r + 2r2 = 24 + -24

Combine like terms: 169 + -24 = 145
145 + -39r + 2r2 = 24 + -24

Combine like terms: 24 + -24 = 0
145 + -39r + 2r2 = 0

Factor a trinomial.
(5 + -1r)(29 + -2r) = 0


Subproblem 1
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5

Subproblem 2
Set the factor '(29 + -2r)' equal to zero and attempt to solve:

Simplifying
29 + -2r = 0

Solving
29 + -2r = 0

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

Add '-29' to each side of the equation.
29 + -29 + -2r = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -2r = 0 + -29
-2r = 0 + -29

Combine like terms: 0 + -29 = -29
-2r = -29

Divide each side by '-2'.
r = 14.5

Simplifying
r = 14.5
Solution
r = {5, 14.5}

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