3r^2=24-r

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Solution for 3r^2=24-r equation:


Simplifying
3r2 = 24 + -1r

Solving
3r2 = 24 + -1r

Solving for variable 'r'.

Reorder the terms:
-24 + r + 3r2 = 24 + -1r + -24 + r

Reorder the terms:
-24 + r + 3r2 = 24 + -24 + -1r + r

Combine like terms: 24 + -24 = 0
-24 + r + 3r2 = 0 + -1r + r
-24 + r + 3r2 = -1r + r

Combine like terms: -1r + r = 0
-24 + r + 3r2 = 0

Factor a trinomial.
(-3 + -1r)(8 + -3r) = 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 + -3r)' equal to zero and attempt to solve: Simplifying 8 + -3r = 0 Solving 8 + -3r = 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 + -3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3r = 0 + -8 -3r = 0 + -8 Combine like terms: 0 + -8 = -8 -3r = -8 Divide each side by '-3'. r = 2.666666667 Simplifying r = 2.666666667

Solution

r = {-3, 2.666666667}

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