12r^2=27+27r

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Solution for 12r^2=27+27r equation:


Simplifying
12r2 = 27 + 27r

Solving
12r2 = 27 + 27r

Solving for variable 'r'.

Reorder the terms:
-27 + -27r + 12r2 = 27 + 27r + -27 + -27r

Reorder the terms:
-27 + -27r + 12r2 = 27 + -27 + 27r + -27r

Combine like terms: 27 + -27 = 0
-27 + -27r + 12r2 = 0 + 27r + -27r
-27 + -27r + 12r2 = 27r + -27r

Combine like terms: 27r + -27r = 0
-27 + -27r + 12r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -9r + 4r2) = 0

Factor a trinomial.
3((-3 + -4r)(3 + -1r)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -4r)' equal to zero and attempt to solve: Simplifying -3 + -4r = 0 Solving -3 + -4r = 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 + -4r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4r = 0 + 3 -4r = 0 + 3 Combine like terms: 0 + 3 = 3 -4r = 3 Divide each side by '-4'. r = -0.75 Simplifying r = -0.75

Subproblem 2

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

Solution

r = {-0.75, 3}

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