r^2-7r=24-2r

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Solution for r^2-7r=24-2r equation:


Simplifying
r2 + -7r = 24 + -2r

Reorder the terms:
-7r + r2 = 24 + -2r

Solving
-7r + r2 = 24 + -2r

Solving for variable 'r'.

Reorder the terms:
-24 + -7r + 2r + r2 = 24 + -2r + -24 + 2r

Combine like terms: -7r + 2r = -5r
-24 + -5r + r2 = 24 + -2r + -24 + 2r

Reorder the terms:
-24 + -5r + r2 = 24 + -24 + -2r + 2r

Combine like terms: 24 + -24 = 0
-24 + -5r + r2 = 0 + -2r + 2r
-24 + -5r + r2 = -2r + 2r

Combine like terms: -2r + 2r = 0
-24 + -5r + r2 = 0

Factor a trinomial.
(-3 + -1r)(8 + -1r) = 0

Subproblem 1

Set the factor '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3

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 = {-3, 8}

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