2(r-11)=(r-5)[(r+3)-13]

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Solution for 2(r-11)=(r-5)[(r+3)-13] equation: 


Simplifying
2(r + -11) = (r + -5)[(r + 3) + -13]

Reorder the terms:
2(-11 + r) = (r + -5)[(r + 3) + -13]
(-11 * 2 + r * 2) = (r + -5)[(r + 3) + -13]
(-22 + 2r) = (r + -5)[(r + 3) + -13]

Reorder the terms:
-22 + 2r = (-5 + r)[(r + 3) + -13]

Reorder the terms:
-22 + 2r = (-5 + r)[(3 + r) + -13]

Remove parenthesis around (3 + r)
-22 + 2r = (-5 + r)[3 + r + -13]

Reorder the terms:
-22 + 2r = (-5 + r)[3 + -13 + r]

Combine like terms: 3 + -13 = -10
-22 + 2r = (-5 + r)[-10 + r]

Multiply (-5 + r) * [-10 + r]
-22 + 2r = (-5[-10 + r] + r[-10 + r])
-22 + 2r = ([-10 * -5 + r * -5] + r[-10 + r])
-22 + 2r = ([50 + -5r] + r[-10 + r])
-22 + 2r = (50 + -5r + [-10 * r + r * r])
-22 + 2r = (50 + -5r + [-10r + r2])

Combine like terms: -5r + -10r = -15r
-22 + 2r = (50 + -15r + r2)

Solving
-22 + 2r = 50 + -15r + r2

Solving for variable 'r'.

Reorder the terms:
-22 + -50 + 2r + 15r + -1r2 = 50 + -15r + r2 + -50 + 15r + -1r2

Combine like terms: -22 + -50 = -72
-72 + 2r + 15r + -1r2 = 50 + -15r + r2 + -50 + 15r + -1r2

Combine like terms: 2r + 15r = 17r
-72 + 17r + -1r2 = 50 + -15r + r2 + -50 + 15r + -1r2

Reorder the terms:
-72 + 17r + -1r2 = 50 + -50 + -15r + 15r + r2 + -1r2

Combine like terms: 50 + -50 = 0
-72 + 17r + -1r2 = 0 + -15r + 15r + r2 + -1r2
-72 + 17r + -1r2 = -15r + 15r + r2 + -1r2

Combine like terms: -15r + 15r = 0
-72 + 17r + -1r2 = 0 + r2 + -1r2
-72 + 17r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
-72 + 17r + -1r2 = 0

Factor a trinomial.
(-9 + r)(8 + -1r) = 0


Subproblem 1
Set the factor '(-9 + r)' equal to zero and attempt to solve:

Simplifying
-9 + r = 0

Solving
-9 + r = 0

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

Add '9' to each side of the equation.
-9 + 9 + r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + r = 0 + 9
r = 0 + 9

Combine like terms: 0 + 9 = 9
r = 9

Simplifying
r = 9

Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {9, 8}

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