35=r(r-2)

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Solution for 35=r(r-2) equation:


Simplifying
35 = r(r + -2)

Reorder the terms:
35 = r(-2 + r)
35 = (-2 * r + r * r)
35 = (-2r + r2)

Solving
35 = -2r + r2

Solving for variable 'r'.

Reorder the terms:
35 + 2r + -1r2 = -2r + 2r + r2 + -1r2

Combine like terms: -2r + 2r = 0
35 + 2r + -1r2 = 0 + r2 + -1r2
35 + 2r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
35 + 2r + -1r2 = 0

Factor a trinomial.
(7 + -1r)(5 + r) = 0

Subproblem 1

Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7

Subproblem 2

Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 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 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5

Solution

r = {7, -5}

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