-2r(5-r)=13+r

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Solution for -2r(5-r)=13+r equation:


Simplifying
-2r(5 + -1r) = 13 + r
(5 * -2r + -1r * -2r) = 13 + r
(-10r + 2r2) = 13 + r

Solving
-10r + 2r2 = 13 + r

Solving for variable 'r'.

Reorder the terms:
-13 + -10r + -1r + 2r2 = 13 + r + -13 + -1r

Combine like terms: -10r + -1r = -11r
-13 + -11r + 2r2 = 13 + r + -13 + -1r

Reorder the terms:
-13 + -11r + 2r2 = 13 + -13 + r + -1r

Combine like terms: 13 + -13 = 0
-13 + -11r + 2r2 = 0 + r + -1r
-13 + -11r + 2r2 = r + -1r

Combine like terms: r + -1r = 0
-13 + -11r + 2r2 = 0

Factor a trinomial.
(-1 + -1r)(13 + -2r) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(13 + -2r)' equal to zero and attempt to solve: Simplifying 13 + -2r = 0 Solving 13 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2r = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2r = 0 + -13 -2r = 0 + -13 Combine like terms: 0 + -13 = -13 -2r = -13 Divide each side by '-2'. r = 6.5 Simplifying r = 6.5

Solution

r = {-1, 6.5}

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