12r^2+21r-2=8-5r

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Solution for 12r^2+21r-2=8-5r equation: 


Simplifying
12r2 + 21r + -2 = 8 + -5r

Reorder the terms:
-2 + 21r + 12r2 = 8 + -5r

Solving
-2 + 21r + 12r2 = 8 + -5r

Solving for variable 'r'.

Reorder the terms:
-2 + -8 + 21r + 5r + 12r2 = 8 + -5r + -8 + 5r

Combine like terms: -2 + -8 = -10
-10 + 21r + 5r + 12r2 = 8 + -5r + -8 + 5r

Combine like terms: 21r + 5r = 26r
-10 + 26r + 12r2 = 8 + -5r + -8 + 5r

Reorder the terms:
-10 + 26r + 12r2 = 8 + -8 + -5r + 5r

Combine like terms: 8 + -8 = 0
-10 + 26r + 12r2 = 0 + -5r + 5r
-10 + 26r + 12r2 = -5r + 5r

Combine like terms: -5r + 5r = 0
-10 + 26r + 12r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 13r + 6r2) = 0

Factor a trinomial.
2((-5 + -2r)(1 + -3r)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -2r)' equal to zero and attempt to solve:

Simplifying
-5 + -2r = 0

Solving
-5 + -2r = 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 + -2r = 0 + 5

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

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

Divide each side by '-2'.
r = -2.5

Simplifying
r = -2.5

Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3r = 0 + -1

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

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

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {-2.5, 0.3333333333}

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