r^2-6r=2r+20

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Solution for r^2-6r=2r+20 equation:


Simplifying
r2 + -6r = 2r + 20

Reorder the terms:
-6r + r2 = 2r + 20

Reorder the terms:
-6r + r2 = 20 + 2r

Solving
-6r + r2 = 20 + 2r

Solving for variable 'r'.

Reorder the terms:
-20 + -6r + -2r + r2 = 20 + 2r + -20 + -2r

Combine like terms: -6r + -2r = -8r
-20 + -8r + r2 = 20 + 2r + -20 + -2r

Reorder the terms:
-20 + -8r + r2 = 20 + -20 + 2r + -2r

Combine like terms: 20 + -20 = 0
-20 + -8r + r2 = 0 + 2r + -2r
-20 + -8r + r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-20 + -8r + r2 = 0

Factor a trinomial.
(-2 + -1r)(10 + -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 '(10 + -1r)' equal to zero and attempt to solve: Simplifying 10 + -1r = 0 Solving 10 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1r = 0 + -10 -1r = 0 + -10 Combine like terms: 0 + -10 = -10 -1r = -10 Divide each side by '-1'. r = 10 Simplifying r = 10

Solution

r = {-2, 10}

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