r^2=2r+24

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Solution for r^2=2r+24 equation:


Simplifying
r2 = 2r + 24

Reorder the terms:
r2 = 24 + 2r

Solving
r2 = 24 + 2r

Solving for variable 'r'.

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

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

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

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

Factor a trinomial.
(-4 + -1r)(6 + -1r) = 0

Subproblem 1

Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4

Subproblem 2

Set the factor '(6 + -1r)' equal to zero and attempt to solve: Simplifying 6 + -1r = 0 Solving 6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1r = 0 + -6 -1r = 0 + -6 Combine like terms: 0 + -6 = -6 -1r = -6 Divide each side by '-1'. r = 6 Simplifying r = 6

Solution

r = {-4, 6}

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