r^2-4r=2r+16

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Solution for r^2-4r=2r+16 equation: 


Simplifying
r2 + -4r = 2r + 16

Reorder the terms:
-4r + r2 = 2r + 16

Reorder the terms:
-4r + r2 = 16 + 2r

Solving
-4r + r2 = 16 + 2r

Solving for variable 'r'.

Reorder the terms:
-16 + -4r + -2r + r2 = 16 + 2r + -16 + -2r

Combine like terms: -4r + -2r = -6r
-16 + -6r + r2 = 16 + 2r + -16 + -2r

Reorder the terms:
-16 + -6r + r2 = 16 + -16 + 2r + -2r

Combine like terms: 16 + -16 = 0
-16 + -6r + r2 = 0 + 2r + -2r
-16 + -6r + r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-16 + -6r + r2 = 0

Factor a trinomial.
(-2 + -1r)(8 + -1r) = 0


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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

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

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

Divide each side by '-1'.
r = -2

Simplifying
r = -2

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 = {-2, 8}

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